Quests

A Class Act
While on Route 6, you encounter another adventurer who is the same trainer class as you are, and both of you want the item sitting on the road. Have a competition between you to see who has better honed the skills of your class and who will get the item. After the competition, regardless of who won, someone will come along, let you know that they dropped the item and then take it with them. From participating in the competition to see who had better skills, you feel more experienced in your class than you did before.
Rewards: 30 Trainer EXP

The Odd Ambush
Your Pokemon are acting strange when you cross into an area surrounded by strange plants. After you wonder what the matter is, the plants pop out of the ground to reveal that they're really Oddish! Use your Pokemon to defeat the ambush and they will grow stronger because of it.
Rewards: 20 Pokemon EXP (to be split between the participating Pokemon as the quester sees fit)

Poliwag's Police
You find a Poliwag while on the route, and it looks friendly, so you play with it. The little thing grows to like you and starts following you. Later on the same road, Officer Jenny stops you to ask you whether or not you'd seen a Poliwag matching the picture she has, because it's missing and its trainer is devastated. You can tell that the Poliwag you have with you is the same one in the picture and turn the Pokemon in to her. She mentions that there's a Yen reward and gives you the money before driving off with the Poliwag on her motorcycle.
Rewards: 600 Yen, 5 Trainer EXP