You guys are going to hate me, but since Politoed has been officially released in the DW and his special moves are known, we can now go into move combination legality issues with Drizzle. Egg moves are fine, gen IV only moves are a problem. He gets Sleep Talk in the DW, however it does not pass down so any Politoed with Sleep Talk can have no Egg Moves so...
Upstart's ~ Rest Talker ~
Encore is illegal with Sleep Talk if you're going to use Drizzle.
I checked every other set suggested and they all look fine.
My opinion about Politoed: Arguably the best weather inducer, and this is not because I am a toed fanboy, I actually like Ninetales a lot better. Here's why the Toed is awesome:
-Good bulk with the best defensive mono type in the game. There are so many weather inducers your personal one needs to survive. Only Hippo does this better imo and that's because he has Slack Off. Drizzletoed's rain interrupts Solar Beam, Grass Knot is only 60 power against him, and Energy Ball has many users, but hits Toed on his bulkier side. Power Whip/Wood Hammer can do a number to the guy, but there aren't a ton of good users (Abomasnow, Venusaur, Tangela come to mind). Just coming out he neutralizes Chlorophyllers' speed boost and possibly their main STAB - Solar Beam (the Beam won't last for long, people will probably run Energy Ball or Giga Drain instead). He is asking to be struck by Thunder, but I've seen very few pokemon that run it w/o rain support (that might become more common however). If your opponent has Rain Support then it really doesn't matter if your toed dies. His two weaknesses can easily be covered by some great rain-abusers, including Zapdos and Nattorei. Lightning Rod and Herbivore can make trying to hit a Politoed SE a big mistake.
-His STAB is SE against all non-rain weather inducers other than Abomasnow. He gets Focus Blast and Brick Break to deal with him. Sun does neutralize his STAB, but Hydro Pump is still SE and 120 BP. Also, running a fighting move on him helps deal with Ttar more easily, particularly if Sand Storm is up.
-Rain is definitely the second-best, if not the best weather (Sand Storm did get some epic improvements with Sand Throw and Strength). Rain is versatile. You don't have to worry about residual damage on your own pokemon if you chose to use other types than water. As a matter of fact, it's amazing with Steel types, neutralizing one of their weakness (though it does virtually give them a weakness to water), and can also be used to help defensive Bug and Grass pokemon with their myriad of weaknesses (just don't use synthesis/moonlight/morning sun). Guys like Scizor, Forretress, and Nattorei become even better with Rain support, as it halves their 4x weakness. In general, water is a great attacking type and can reach near perfect neutral coverage with just a normal move (Nattorei kind of screws that up this Gen). Other than Sand-Strength Bullet Punch (which I'm not even completely sure exists), Aqua Jet is the only weather-boosted priority, and it has a ton of great users. I can't really argue too much against Sand Storm, but sun teams can be dubious because most Chlorophyll users are weak to fire, Solar Beam is easily dealt with by another weather-inducer (whereas Thunder and Gale still has a 70% chance to be effective even if the weather is changed), and though Fire pokemon do lose their weakness to water in it, they are still weak to Rock and Ground -- two very common types. Hail's short-comings are pretty obvious, so I won't go into them.
I don't think Kyogre and Politoed should be compared. I feel like it's pretty obvious Game Freak gave these abilities to Toed and Tales so these weather effects would be more prevalent in standard play. Leaving Smogon's tiers out of this, Kyogre and Groudon are banned from almost every local tourney I've been to (allowing ubers in locals only attracts little kids lol) and this year was the first year Nintendo's VGCs allowed them (in recent memory, I don't know much about gen 3 VGCs).
I hope I made some valid points ^^.