You can have fun with this.
Essentially everything. So let's not say the mayor is evil, just as you say, a child of privilege who throws a tantrum when things don't go his way.
When the PC's get back, they find:
1. That most of the villagers are divided into a pro-mayor, against-mayor camp. Those against-mayor will be angry with the PC's for giving him that position, but will be very vocal in their grivences to the PC's too.
2. The pro-mayor group will be people who are close friends to the mayor and have gotten all the best deals, decisions, choice crops, lowest taxes, etc. You name it, they are kissing the mayor's butt and riding the gravy train.
3. The mayor has botched up a job on handling outlying farms falling to bandits and goblins. They will find some of the farmers who are homeless and begging for food and scraps at the local church because their farms got raided and they escaped with their lives. When the PC's inquire about it, the mayor didn't send the manpower to go deal with the bandits / goblins because he likes having guards hang around him for personal protection.
4. The good and honest sheriff was sacked and sent packing for speaking his mind. The constables now take orders directly from the mayor and they are doing what they can to hold onto their jobs. If the sheriff was in control, the bandits and goblins wouldn't have been a persistent problem.
5. They find out that a festival that the whole village normally celebrates was moved to the mayoral mansion and only the closest mayor's friends are celebrating, everyone else has to work. This does not make for happy villagers. The PC's arrive at the village at the time when they know there should be a festival in full-swing, but see only empty streets.
6. The mayor has been having party after party and the village's coffers have been completely spent and is deep in the red. Money lenders are hovering in the village and they are bringing some nasty toughs to collect payment in which if they don't get paid, they may start taking things from the locals first since they are easier targets in order to collect their due. You can make this a more legitimate claim by allowing the money lenders to foreclose on other local villagers and confiscate their belongings and the PC's have to deal with that mess.
7. The grain stores which the villagers contribute to tide themselves over in winter is completely spent because the mayor gave it out to "friends" who came from all over the place and as gifts got to take away lots of grain sacks along with other goods. The bad thing is that the mayor kept this a secret and the villagers don't know that they face starvation come winter.
8. The relationship with the druid circle has taken for a turn for the worse, when the mayor starting cutting extra trees breaking their village's agreement after 200 years of peaceful trade. Now the druid circle refuses to come and bless crops, fertility in the livestock, etc.
9. Trappers and huntsman won't come to the village until they've been paid the money due to them for the pelts, furs, and meat they provided. The PC's take note when they visit the inn and there is no meat for the meals and the butcher has closed shop. The mayor has ignored them thinking their fees are ridiculously high and offered a contract for coppers on the gold piece which they immediately scoffed at and left.
10. The local blacksmith was thrown in jail for not giving a gift to the mayor on his birthday. His sentence is 30 days.
Have fun!
