First of all, the 3 things I really loved in Halo 3 (and something I wish every other game will have):
1: Saved films are awesome. It's definitely a "wow" moment the first time you watch a saved film, freeze the timer and just have a look around the scene. It's a lot of fun just watching memorable moments and try to take fancy screenshots of them. My only complaints about the feature is that it lacks a functon to "bookmark" specific moments or being able to skip to certain parts of the video (playing through a video which is one hour long to try to get to one specific scene is a chore).
The saved film feature just makes me feel I'm suddenly pushed 10 years back into the past. Remember the early FPS games? Doom? Duke 3D? Quake? It was pretty much taken for granted replays was a feature you could expect in FPS games (and a few other genres) back then. So it's nice to again have a game which supports replays (and makes it much more awesome by being able to freely move the camera and easily change the replay speed).
2: Scoring in singleplayer. If replays takes me back 10 years, I suppose scoring takes me back 15 years. Scoring is a really simple feature but it's surprisingly fun. With a score in the bottomright corner of the screen you suddenly feel compelled to do better and it's fun to compare scores with other players. My only complaint about the scoring system is that I couldn't actually find a highscore list within the menus (my other complaint is that I incorrectly assumed scoring was only available after you completed the game... although that was purely my fault. To anyone else, just remember to start a campaign via the "Campaign" on the main menu and not "Start New Solo Game", the former button lets you activate scoring.
3: 4-player coop. I actually haven't been able to try 4-player coop yet, but the very idea of it is pure awesomeness.
All those 3 features are something I'm really hoping will become common features in other games. And it's definitely those things I'll remember when thinking back to Halo 3.
Now as I've talked about the good stuff, time to talk about the bad...
The singleplayer campaign is too darn similar to Halo 1 and 2. I suppose hardcore fans of Halo will eat it all up. But compared to other modern shooters, it's really nothing special. The game feels like it's repeating itself a lot, and after playing recent games like MoH:A and Bioshock it definitely feels like a step backwards to deal with linear level design where you're limited how you approach a situation.
One thing annoys me is that it mindlessly duplicates some of the quirks of earlier Halo games. The starting levels (and a few later levels) are crawling with snipers who can kill you instantly (on Heroic or Legendary). It's really frustrating to slowly clear a zone of enemies and then suddenly getting insta-killed by a sniper who's near impossible to see. And then you need to spend a half hour doing that part of the level over again.
Another returning annoyance is the Flood. The level where they're introduced isn't bad. It's a refreshing variety based on the previous levels... but well, that one level would have been far more than enough.
And there's a new problem in Halo 3 I didn't have in Halo 1 and 2. You'll rarely find new ammo for your current weapon so you'll have to keep picking up different weapons from enemies. This alone isn't so bad. It's actually rather fun constantly using new weapons. But with certain checkpoints this becomes a really frustrating element. There's a few checkpoints where you have to walk for quite a bit to the next encounter which happens to be dreadfully difficult and if you happen to have poor weapons/little ammo then you're screwed. It can be compared to quicksaving while you're low on health right next to an enemy shooting at you (of course, not possible in this game, but can happen in many other shooters but it feels equally frustrating as re-starting a difficult checkpoint with bad weapons).
The one thing which makes the gameplay feel different from Halo 1 and 2 is the equipment. Unfortunately, I don't think Bungie implemented it that well. The AI is able to use them but they seem to activate them at completely random times (a few times they even activated equipment where it would benefit me instead of them). Some of the effects by the equipment are nice, but the equipment themselves are just too rare. You can only carry one at a time, and you'll rarely find new ones. I think equipment might actually work really well in multiplayer, but in singleplayer I found them to be a trivial addition.
The presentation of the game feels rather bland as well. It takes ages before the storyline actually progresses, and the constant one-liners randomly uttered by Cortana really becomes tiresome. It seems the storyline depend too much on the player having a massive erection for Master Chief and Cortana, and if you don't you really don't care about the story at all. (just imagine Star Wars, only with 90% of the plot removed and Darth Vader is played by Vin Diesel and Padme is played by Britney Spears... that's how the Halo 3 story feels like)
The music would have been great if it weren't for the fact I already heard it in Halo 1 and 2. There's too much music which is mere remixes of older tunes. I actually can't remember hearing any new tunes.
The graphics are good, but certainly not a major step up compared to Halo 2. It reminds me of how the graphics from Dead or Alive 3 improved in Dead or Alive 4. I get the impression they focussed on keeping the "Halo style" so it doesn't look vastly different. Although there are a few cutscenes with spectacular lighting where the game looks really amazing.
I haven't tried multiplayer yet, but I was definitely impressed by all the multiplayer options this game presents. It feels like a mini-mod function with how you can change so many variables for a gamemode.
So, my overall opinion about Halo 3 is that replays and coop are awesome, the rest is poop. And that Bungie should make a new Myth game. Please.