FIDDLESTICKS IS ALSO GOOD ON MID!
It is still a good stallbreaker (Jellicent can do a similar set, and has better typing; but it's too slow and has less physical defense; cannot outrun Tentacruel except if it max invests in Speed, but it has to sacrifice bulk for this). The only thing that poses a problem for Mew on stall teams is Heatran, and even then, you can easily solve this using Aura Sphere/Seismic Toss instead of Psychic, or partner it with a Dugtrio.
While it appears to be outclassed by Celebi on the Nasty Plot department, Mew has a big advantage over Celebi: as it can use Psyshock, it can easily bypass the pink blobs. Celebi can only do this at +6 with Giga Drain, but Celebi risks being either paralyzed, thus stopping its sweep, or it can be Toxic stalled. Celebi can only safely setup on the pink blobs without having its sweep stopped cold if it's burned, but due to Natural Cure, it's hard to have a burned Celebi. Unless for some reason you run Heal Bell (I've already did this) you can easily break through the blobs, but you sacrifice coverage if you do this. I still think that Celebi has more advantages over Mew than Mew has over Celebi, but that doesn't mean that Mew is outclassed.
Lastly but not least, Mew can run a Baton Pass set. Celebi can also do this, but it lacks a way to boost Speed (Mew has Rock Polish). Gorebyss can easily pass Shell Smash, but Mew can boost and doesn't have to lower defenses; it doesn't need to run White Herb for this, and thus can use Leftovers, increasing its survivability.