: It can be caught in the Pokemon Mansion in all three games, but is much easier to find in Blue and Yellow
: Above average HP and Attack, middling Defense, and horrible Speed and Special.
: He should only be a few levels aways from Sludge when you catch he if he doesn't have it already. That's important, because it's his only STAB and most of his usable TMs run off his bad Special. When you need to seriously consider running Mimic, you know your movepool is horrible. If you haven't used the Body Slam TM yet, Muk can make decent use of it. Without it, you'll be forced to run crap like Toxic or Screech in the fourth moveslot.
: Grimer blows (especially that late in the game), but should be pretty close to evolving to Muk if you didn't just catch the evolved version to begin with. Sludge can actually do some decent damage thanks to Muk's 105 Base Attack. That said, 99% of teams will carry something that can do more damage to any given threat by the time Grimer is available. Grimer's biggest problem comes from the fact that Poison hits almost nothing relevant for SE damage by the time you get him.
: As touched on in the last section, Poison is a horrible typing. This is made worse because by the time you catch him, there aren't really any more Bug type or Grass type pokemon to prey on, and most of the important fights put him at a big disadvantage.
Blaine- Muk can't really trade blows thanks to his low Special and low BP STAB.
Giovanni- This is a horrible, horrible idea. Don't even bother trying
Lorielli- Gets hit on his Low Special all match, and can't really threaten anything she has.
Bruno- Muk can beat all three Fighting types in both versions, as long as your level is higher than his Machamp's to negate the threat of Fissure.
Agatha- All five pokemon resist your STAB and three are immune to Normal moves. So no.
Lance- Muk can take a Hyper Beam and multiple Dragon Rages from the Dragonairs if you're desperate, but Gyarados and Aerdactyl beat him and D-Nite probably will as well. In Yellow, everything beats him.
Rival- Muk can trade blows with Venusaur if you picked Squirtle. That's about it.
: Muk could probably be bumped up a tier if it didn't come so late. Unfortunately, by the time you get him his typing is a big hinderance and there are many better options. You could technically beat Koga early and Surf down to Cinnabar to get it earlier, but it's really not worth the extra effort. Disappointing.
EDIT: If for whatever reason Low and Bottom are re-separated, I'd put Grimer in Bottom.