Best season to move to Costa Rica

What is the best season/time of the year to move to Costa Rica, and why?
The best season would probably be December to April when it is less rainy, just in terms of not getting wet. 

How do rent prices fluctuate based on the different seasons?
I don't know for sure but pretty sure most people would offer unrented places for less in the rainy season (see above).

Is there a change in the job market depending on the seasons, such as job availability?
There really is no "job market" here as far as I know. If there is, it would be for telemarketers, the online gambling industry or illegal hospitality jobs (i.e. illegal in that only Ticos or permanent residents can work here legally.
As to "regular jobs" you'd have to be sponsored by a company to legally work here which usually means you'd have to have a very special skill set that a Tico could not fill.

Are there any seasonal festivals or cultural events that would allow you to learn about the country?
Ticos are always having some kind of festival but I'm not much interested in crowds and loud music so I don't go. Someone else will have to answer this one.

What are the times of year to avoid for expatriation to Costa Rica?
See above re moving in rainy season. But there's really no time to avoid other than rain as far as I can see.

During which season did you move? How did it go?
I moved at the end of the rainy season in November. The move went well.

One note is that you can't just "up and move" to Costa Rica unless you want to be an illegal resident, or perpetual tourist. Perpetual tourist means you leave the country every 3 months then come back in 15 min later or whatever, to get your passport stamped with a new 90 day stay (no guarantee you'll get 90 days , you may only get 30, but that's unusual in my experience).

Some say it's illegal to be a perpetual tourist but all I know is, I've known several people who did it for more than 10 years and one who is still doing it and never has a problem with it. The only problem (unless you are unlucky and get a border official on a bad day who won't let you in; again, almost unheard of) is the hassle of driving or flying out of the country every 90 days and coming back across.