There was this Ace Trainer on Route 1 with a Starmie. It creamed Lapras and Vileplume with some attacks I can't even remember, and only went down after Espeon took it out with Shadow Ball. I really should have been using Espeon in the first place…
Also, Lance. His Aerodactyl wiped the floor with two-thirds of my team, thanks to Rock Slide, the move's side effect of making the opponent flinch, and everyone on my team being slower than it. Ampharos finally put it away with Thunderpunch, though it was partly due to luck, since it somehow didn't flinch against Rock Slide while everyone else on my team did.
His Dragonites, on the other hand, were a minor obstacle at best.
Karen was somewhat annoying. I ended up making a pretty dumb move and used Typhlosion's Flamethrower just as she switched out to Houndoom (which, of course, activated its Flash Fire). Her Gengar also cleaned my Ursaring's clock thanks to Destiny Bond. Umbreon wasn't an issue for me, since I had three moves on my team that could hit with perfect accuracy (Typhlosion's and Espeon's Swift, and Ursaring's Faint Attack).
Surprisingly, I had little to no trouble with Whitney's Miltank this time around. I had no super-effective moves, but I used my Quilava's Defense Curl and Smokescreen to render that Miltank practically useless. Miltank's Stomp and Rollout did next to no damage (even Rollout, which was super-effective), its Attract was useless, and its moves missed almost all the time (which reset Rollout's power back to its minimum every time). The only annoyance was Milk Drink, but Miltank eventually went down thanks to a burn and a well-timed critical hit.