I've only played turn-based games, so I can't comment on any real-time features.
For me, a big pro is the Tactics Trainer; it's a large part of why I got a paid membership when I started getting back into the game a couple months ago.
At my level of problem (1200 +/- 100 right now), I haven't run into the sort of incorrectly-marked-wrong answers that others have commented on more than a couple times. Typically, if I go for a "good" move that gets marked wrong, when I look a little longer, I see that I missed a better move. Taking a rook free versus seeing mate in two is useful in training vision for me. I have a list of "things to check" that have come out of such "errors."
I like the game analyzer as well, for showing me different/better lines.
It could be that stronger players are dealing with nuances that make these tools less useful, but at my level they are wonderful.
I appreciate that I can easily indicate I'm looking for a game, and that the community is big enough that I get a taker pretty quickly.
If I had to pick a con it would be the performance of the iPhone app. It's not bad for me usually (definitely better than nothing), but it does seem slow. And not having access to my game notes has been an issue in the past. I'd also like to have access to the Computer Workout feature in the app, but that's a wish list thing.
What greater "pro" can there be than the fact that the site is free (if you want it to be)? I even like the way you are sometimes reminded that you could pay - to me this is a reminder that yes, indeed, I don't have a trial membership which is about to expire...I am actually a member.
As for restrictions pertaining to non-paying members, such as only being able to do three tactics-trainer puzzles per day: better to complain about this than to complain about not being able to do any at all.
Finally, as for advertisements: I have no problem with them at all. In fact, I hope this site is making good money despite making its most important feature - being able to play chess via the internet - essentially free. If they took away the advertisments and forced a membership fee, then I would complain...and so would most of you I bet :)