Viable Uses for Mew?
I'm gonna go ahead and assume that "Mythical Pokemon", like Legendary Pokemon, are not allowed for Gym Defense.
So let's talk offense.
Normal Type is useless on offense, and any Psychic, Grass, Fire, Fighting, Rock, Steel, Electric, Bug, or Poison moveset is outclassed by other options.
So what does that leave us with?
Well, with Frost Breath and Blizzard, Mew could actually become one of the best Ice Type attackers in the game, at least till Mamoswine is released in Gen 4, however long from now that is. Walrein, Cloyster, and Lapras all have very poor attack stats, and even Articuno's attack stat is less than 200. Jynx's is 225, but she's pretty frail. Mew's is a decent 210, which is 15 points less than Jynx's, yes, but Mew gets much more solid bulk for that loss of power.
In addition, Mew gets access to the coveted Shadow Claw, which right now is only limited to legacy Gengar (which gets ripped apart by Psychic type targets because of its awful poison second typing) and Banette (which has the defensive stats of wet tissue paper). Although Mew doesn't get type bonus, Shadow Claw is still highly potent. With SC and Dark Pulse, decent bulk, and with a natural resistance to Psychic, I could see Mew becoming a great killer of psychic type raid bosses.
Answers
I'd be interested to see two of the best quick and charge moves in the game mix together- Shadow Claw and Grass Knot/Energy Ball/Wild Charge.
Sure they provide 0 type synergy and omitting stab but it's interesting to see what cycle DPS you can create with these.
Edit:
Snarl+Dark Pulse looks like a legit psychic counter for the focus blast contingency (obviously Ttar is still better otherwise). Doesn't run into the same problem as mewtwo for having a resisted quick move.
Mew doesn't get STAB, so when we're comparing it to ice types for example, Mew's effective base attack is 210/1.2=175. That gives a good idea on how good its ice DPS ie. not that good. Mew is pretty solidly between Walrein and Lapras both in DPS and in bulk, so I guess it's pretty decent if you manage to score the moveset.
