In almost all situations, Mr. Mime is a very poor choice in OU. In terms of stats, ability, and movepool, Alakazam and Espeon are almost completely superior. However, Mr. Mime's ability, Soundproof, gives it a niche on full Baton Pass teams, as it gives Mr. Mime immunity to Perish Song and Roar. In fact, it's the only Pokemon with access to both Soundproof and Baton Pass, and therefore the only good answer to Perish Song that Baton Pass teams have.
In some ways, Mr. Mime fits very well onto a Baton Pass team. Its movepool for Baton Passing is exceptional, including Calm Mind, Nasty Plot, and Barrier for boosting; Taunt and Encore for support; and of course the obligatory Substitute and Baton Pass. Mr. Mime's Special Defense is also excellent, so in conjunction with Calm Mind, Mr. Mime can wall almost every special attacker. However, Mr. Mime's Psychic typing is far from ideal, bearing in mind that Espeon is mandatory for Baton Pass teams, and Mew and Celebi are also very strong Baton Passers. Mr. Mime's physical frailty is a severe drawback, and only further compounds the weaknesses of Espeon. Altogether, though, Mr. Mime is a reasonable Baton Passer even when there is no threat of Perish Song, and as such is a staple on dedicated Baton Pass teams.
This set is designed for use on full Baton Pass teams, acting as a special wall and Calm Mind passer. Mr. Mime can boost its already excellent Special Defense even higher through the use of Calm Mind, preventing most special attackers from breaking its Substitutes. Keeping a Substitute up is absolutely critical to Baton Pass teams, as it protects them from critical hits, moves such as Trick and Thunder Wave, and for that matter any unexpected attacking move. Be warned that you still need to watch out for Dragon Tail, as it is often strong enough to break Mr Mime's Substitutes. Encore is the preferred option in the last slot, as it gives your team an answer to setup sweepers, and can be used to prevent unwanted moves such as Taunt. With the opponent locked in, Mr. Mime and its teammates should find it very easy to set up boosts.
The main reason to use this set is that Mr. Mime's ability, Soundproof, provides an answer to Perish Song, a move that otherwise almost completely counters Baton Pass teams. To clarify, Mr. Mime is immune to the move itself, rather than to the Perish counts, which it can still receive, pass on, and succumb to. This is not a problem, though, as Mr. Mime deals with the most common Perish Song users, Politoed and Celebi, rather well. You'll need to switch into them before fully knowing their sets fully, but Mr. Mime can take even a Choice Specs Politoed's Hydro Pump at full health and Baton Pass back out again. Soundproof also gives immunity to Roar, which helps to take some pressure off Espeon (a fixture on Baton Pass teams), and Bug Buzz, which helps a lot against Volcarona. Mr. Mime is a surprisingly good answer to it, as Mr. Mime can Encore Volcarona into Quiver Dance and take its Fire attacks reasonably well.Team Options & Additional Comments >>>
If you are considering Mr. Mime for anything other than a Baton Pass team, you are better off using Alakazam instead, as it's stronger, faster, and has Magic Guard. There are a few lesser options that weren't mentioned for the Baton Passer set, though. Hypnosis, Thunder Wave, and Confuse Ray can cause general disruption and provide setup opportunities. Other attacking options are available, such as Signal Beam and Hidden Power, if you want an attack nothing is immune to, but they won't be as generally strong as Psychic and Thunderbolt.
Checks and Counters
Countering Mr. Mime on its own is not at all difficult. After all, the set listed doesn't even have any attacking moves. Countering full Baton Pass teams is another matter entirely. Just slapping any old Taunt, Roar, or Perish Song user isn't going to cut it. However, using a phazer or Taunt user that can heavily damage Espeon (and Mr. Mime) is still very helpful. A Taunt or Roar Tyranitar, for example, will beat Baton Pass teams almost single-handedly. Even Skarmory and Hippowdon can do good damage to Espeon with Brave Bird and Earthquake respectively—it might not go down the first time, but it will go down eventually. Priority Taunt users, such as Sableye and Tornadus, are also pretty much full stops to Baton Pass teams, especially if they can come in on a Pokemon with no attacking moves like the given Mr. Mime set. Some setup sweepers can boost alongside the Baton Passers and emerge victorious, although Mr. Mime's Encore can be problematic for them; good examples include Swords Dance Scizor, Dragon Dance Dragonite, and Quiver Dance Volcarona. Make sure to attack Mr. Mime if it comes in rather than continuing to boost. Cloyster performs strongly against Baton Pass teams thanks to its strong setup move and ability to break through Substitutes with Icicle Spear. However, it has major problems with Vaporeon, which is present on most Baton Pass teams. Lastly, Haze is a move that serves almost no purpose other than to completely counter Baton Pass teams—if you really need it, it's there.