I do have some criticisms, but overall I am really happy that the show has returned, and that the people working on the show have done a worthy job.
If you have not seen the finale, beware that I will be including spoilers here.
In no particular order:-
Doctor's #9 and #10:
I really loved Christopher Eccleston's incarnation. The character had a dark, unsettling edge about him that reminded me of Colin Baker, but also had a lot of charisma which Colin's incarnation did not have. He did have a wonderful "alien" feel about him while also having a "human" side to his character. I can understand Eccleston wanting to avoid getting typecast (as Tom Baker did), but it seems a tragedy that he only stuck around for a single season. With a bit of longevity he might have become my all-time favourite...
It took me a while to warm to David Tennant. At first I thought he was annoying because it seemed that Ecclestone's intensity was replaced by some fairly weak jokes. That weak joke aspect seemed to have an uncomfortable contrast against the random threats the Doctor seemed to make every other episode of bringing down the universe if the villain-of-the-week harmed his companion etc. That's what I thought was bothering me, but then I worked out that this was not the core issue. It comes down to the chemistry between Rose and #9 vs #10. I thought Rose matched up really well with Eccleston, but there's just something wrong about it with Tennant. I only worked this out when I got to Season 3 and found David Tennant to be very enjoyable traveling with Martha even though Season 2 had better writing.
I have decided I like Tennant quite a bit now, and what really blew me away was hearing his (native) Scottish accent on DW Confidential. I had no idea! I am quite happy he ain't dead yet, but it's still a mystery on whether he will be back for Season 5 (he is only confirmed for the next 4 specials between now and the next season).
The Companions:
I've liked them all -- Rose, Martha and Donna. As I said, Rose was much better with #9 than #10. I felt Martha had a lot more potential as a "smarter" companion, but unfortunately she got sucked into the Russell T. Davies vortex of paramilitary organisations and resistance movements. (So did Rose, but at least she got two seasons). Donna was a good change of pace, but unfortunately the writers did not seem comfortable exploiting Catherine Tait's comedic talents (only exploited a handful of times throughout season 4).
I did enjoy how RTD would also get more involvement from the surrounding family (Mickie and Jackie grow on you quickly enough), but with three companions over four seasons where you are getting so involved with their families, it's probably a bit much for it to continue this way. I mean, we are talking Doctor Who, not East Enders.
A final comment on the companions: sentimentality has it's place in the new Who, but when they start to go into hero-worship mode, I start to feel like I'm watching fan-fiction rather than DW.
The Writing:
As happy as I am with Russell T Davies in bringing back Who as such a high quality production, more than half of my bottom ranked stories (see Worst Stories below) are written by him. I think he's a very genuine Doctor Who fan and has a very good grasp of the history and stories of the show, but sometimes he's too much of a fan (see my previous comment on hero worship).
What does really bother me is lazy writing, which happens all-too-often with RTD. The Sonic Screwdriver might as well now be an amulet of wishes that doubles as a stun-gun, on top of also introducing "Psychic Paper" and the "Superphone". Where these items get used are genuine opportunities for creative writing, but RTD falls back on the plot devices. Even in aid of moving the story along at a brisk pace, he leans on these gadgets far too often. I can think of a few other plot devices not tied to gadgets, but the worst of them all was the Dalek "Temporal Shift" plot device. You get how these powers might have eventuated as you learn more about the Time War storyline, but these are such unnecessary and unsatisfying developments given how capable we already know how menacing the Daleks can be. (Terry Nation would be turning in his grave).
This makes it sound like I hate RTD, but I don't. He's created some great storylines, and I have enjoyed a number of the creatures that he has newly introduced into the DW pantheon, but overall I just see him more as a great producer than a writer.
On the other hand, Steven Moffat has written some terrific gems over the last four years, and the good news is that he will be taking over as head writer of the series in 2010. So RTD leaves the show in good hands, and hopefully it gets even better.
Old Villains:
I love the old villains, but I do have to say that the new versions are not as terrifying as compared to the Jon Pertwee/Tom Baker era (the Autons, the Daleks, the Cybermen, the Sontarans). The Daleks, in particular, get too much airtime (often 3 episodes out of a 13 episode season). They are the ultimate enemy, but in the old days whenever the Daleks would appear you knew the story was going to be special. I did like the mind games that Davros was playing with the Doctor in the Season 4 finale -- my favourite Dalek moment from the new Who.
Of the old villains brought back, the writing that featured the Master was the biggest waste. Why is this? All incarnations of the Master are fiendish, have machavellian cunning, and ultimately show psychopathic traits, but you never see humour from the Master. Think about Terror of the Autons, The Deadly Assassin or the Keeper of Trakken -- the Master was pretty terrifying, and he didn't try to crack too many jokes as he hatched his plots; to the contrary, he was a very serious psychopath. In the Season 3 finale, even though he was never short of an answer and consistently had an upper hand on the Doctor all the way to the end, the humourous aspects inherent in the Master's behaviour failed to convince me we were viewing the character originally played by Roger Delgado.
New Villains:
Generally I've really liked the new villains such as the Ood, the Judoon and the Slitheen. I also really enjoyed Simon Pegg's all-too-brief appearance as The Editor in The Long Game.
Hopefully we never see (or even hear of) the Sycorax again.
Favourite Stories:
I think the writing was generally pretty good in Season 1, and my favourite was The Empty Child/The Doctor Dances two-parter. Quite a good story, and Captain Jack Harkness gets a great introduction as a cool character. Generally speaking, because I liked Christopher Ecclestone so much, I might have overlooked inconsistencies throughout the season that would otherwise bother me.
Season 2 also had fairly strong writing, and I know a lot of Who-fans really loved School Reunion -- I also liked it, but I didn't rate it as the season's best. The Girl in the Fireplace is one of my favourite DW short stories of all time, and the best word I can think of to describe the dark two-parter The Impossible Planet/The Satan Pit is "gripping". Fantastic old-school writing there.
The highlight of Season 3 was the Human Nature/The Family of Blood two-parter. The scarecrows had a creepy feel that reminds me of the Jon Pertwee days, and I thought Harry Lloyd was brilliant as Jeremy Baines (the troublemaking, villanous and appropriately creepy schoolboy).
Finally, Season 4 seemed pretty flat in it's writing to me, but Silence in the Library/Forest of the Dead was a real standout as the best of the new series. You know that the fans will be begging to see River Song again, but in a way it would be a shame to get that type of closure. Along those lines, I will say that I did like the finale, but I'd also say that it really tied things up a bit too neatly for my liking. However, considering RTD's contributions to bringing Who back, and impending departure, I can overlook what is obviously a self-indulgence.
Worst Stories:
As I said before, I really quite liked Season 1. Maybe I would rate Father's Day at the bottom, but that would really have much more to do with inconsistencies and some really obvious plot holes that get opened up, which the writer doesn't bother to address. But as a storyline it was worthy of exploration, so I don't want to be overly harsh. I will say the Bad Wolf appearances throughout the season were more annoying than intriguing.
In Season 2, I didn't like Tooth and Claw all that much, but it has nothing on Love and Monsters (possibly the worst of all time?) or Fear Her -- both of which clearly fall into the fan-fiction bucket, and are not worthy of further discussion. Ever.
While there were a few stories in Season 3 that I just found weak (The Shakespeare Code, The Lazarus Experiment), the finale left a really bad taste in my mouth. The overarching idea behind the three-parter was a good one, but I think the detail really let it down. Actually, I loved Utopia which set the scene for the other two episodes beautifully, but I just thought the "Saxon" incarnation of The Master was such a pale imitation of his old self, and I would absolutely hate to think that this is the end of one of my favourite DW villains. The whole "Saxon for PM" storyline was not at all convincing, which I think has much more to do with writing than acting (John Simm is terrific in Life on Mars, and would love to see him playing a different DW character). On the positive side, I will say that I did think the Face of Boe twist was one of the best ever.
With Season 4, I found The Unicorn And The Wasp quite tedious, The Fires of Pompeii plain boring, and The Doctor's Daughter a wasted opportunity to really explore what could have been an intriguing storyline. I also noticed they areally started to go over the top with technobabble in many of the episodes.
Christmas Specials:
The Christmas Invasion may challenge Love and Monsters as the worst ever, but for different reasons -- absolute laziness with the writing, the lameness of the Sycorax, the sword fight... (Maybe this is the reason David Tennant's incarnation got off on the wrong foot with me?)
Fortunately, the other Christmas Specials have been quite good, and Time Crash was a treat.
Final Thoughts:
I read this excerpt in an interview with Steven Moffat (who will be the lead writer when DW resumes in 2010):
Gareth Roberts, who wrote "The Unicorn And The Wasp," has a theory: You write Doctor Who as you remember it. He remembers it as funny and clever, so he writes that kind of Doctor Who. I remember it as being scary.
Excellent :)