The last story mission is extremely awesome because it takes you from fighting on foot to riding a motorcycle to hijacking a plane to kill the last bad guy. In short, it is basically everything cool about the game in one mission.
Boulevard Baby is a well liked mission in that you actually get to see the inside of Bahama Mamas during the mission. The club playing TBOGT version of Radio Vladivostok and the flashing lights and background makes it very fun to watch. Too bad this is the only time you'll ever see the inside of Bahama Mamas.
Demonic Spiders: The Molotov Cocktail wielding gangsters during the Drug Wars. Because the gangs in these missions start off neutral, you will not likely notice them until they land a hit on you while you are distracted by gun wielding enemies. If you get hit by one, you will lose about a third your health and will cause you to be stunned for a few seconds, leading to other enemies to land shots on you. God help you if another molotov cocktail enemy lands a hit...
Game-Breaker: The automatic shotgun (with explosive shells) mentioned below. All the hitting power of a shotgun, with none of the range limitations, combined with Incendiary Exponent. It can blow up a car or a helicopter in two shots.
Genius Bonus: When Mori beats Brucie in the chess game it is a recreation of famous Karpov-Kasparov 1985 World Championship Match.
Hilarious in Hindsight: Just one year after the expansion was released, The Expendables featured the exact same model of automatic shotgun also loaded with explosive rounds to very memorable effect.
Internet Backdraft: When Rockstar announced the title and that your character Luis will be an assistant to the titular Tony. Cue much homophobic whining about how Rockstar "made the series gay".
Jerkass Woobie: Brucie Kibbutz. He's been picked on by his older brother for years. Not to mention Luis genuinely feels sympathetic and sad for Brucie.
Love to Hate: Ray Bulgarin, again. Sure, no one can deny that he is unpleasant and made several horrendous crimes because he enjoyed it. But curiously has several fans, for his voice and some of his lines who is considered entertaining or even funny.
Mori isn't well liked by the fandom at all. Put all of Brucie's overconfidence without the charm and humor, add Napoleon complex, jerkassness, and no Morality Pet, and you'll pretty much get a good idea of what Mori is like.
Some people see Luis's mother as an ungrateful bitch who does nothing but try to guilt trip him and makes it very clear that he's The Unfavorite in the family.
That One Achievement: "Bear Fight" is pretty damn hard to get, considering that the game's melee system isn't so great. Even if you take breaks between fights (which has you betting against two fighters in the ring) to restore your health, the last round is really hard with those fast knife fighters. To make it worse, you cannot, use weapons, use your phone to use health cheats, or even save the game between fights.
"Going Deep". After a very long car ride, you have to fight off wave after wave of heavily armed, heavily armored NOOSE agents in a parking garage, and you only get partial body armor(if you enter a Stockade vehicle). And if any of the agents get close, they will tear your health bar to shreds. It's strongly advised you save some explosive shotgun ammo for this mission to make it less hair-pulling.
Likewise, "In The Crosshairs", which involves fighting your way across several rooftops through an army of guys with automatic weapons and grenade launchers, fending off the occasional helicopter attack, and then jumping down a fire escape to street level, where there are yet more gun-toting goons, stealing the nearest car and driving away until the mission ends.
"Caught With Your Pants Down". Yusuf has you acquire an APC, which, unfortunately for you, is suspended high above the city from a sky crane. He expects you to have the Improbable Aiming Skills needed to snipe the cables holding up the APC from a moving helicopter. When you finally do get past all that, you find that the APC is a bit of a letdown, seeing how it's not completely Immune to Bullets, and will take damage from Stuff Blowing Up too close to it, so you have to deliberately hold yourself back from going apeshit with it.
Most of the helicopter missions tend to be like this considering the awkward handling of helicopters. In particular, "Sexy Time" could be this for many fans, as you have to aim downward and maintain both low altitude and distance to hit the boats that are running away, while dodging RPG fire. Because of these mechanics, it's very easy to crash the chopper into the ocean. In addition, the forums often have contradictory advice regarding how to deal with the mission. Many users have compared this to GTA: San Andreas' infamous (but optional) mission "Supply Lines".
They Wasted a Perfectly Good Plot: After being introduced to the fight clubs in order to pay off Luis' mom's debt, Luis tells her to stay away from the local loan shark. The player can later get a call from Luis' mother where she talks about how nice and well-behaved the loan shark is, so you may expect a mission where Luis has to save his mother again from the loan shark, permanently this time. But no, this never happens. Of course, you do have the option of winning the fight and killing the loan shark to complete the mission.
The back of the box also makes it seem like a tale of a man deciding to stay with the rich and glamorous, or helping out his family and friends in his old neighborhood. This little plot is quickly abandoned in favor of getting out of debt and wrecking Bulgarin's shit.
Luis vows to murder Rocco later during the game, yet this never happens and he doesn't even appear as a random stranger. Was later rectified in GTAV where he gets killed by Michael de Santa.