We are considering renting out our house in the Placencia area to friends and friends of friends for short periods of time. Do we need some sort of permit or approval from the government if we shoud do so?

Rentals having a duration of less than six months are governed by the Hotel Act.
Belize Tourist Board can answer your questions about how to become licensed, taxes due, minimum standards, etc.
In brief - hotel licenses are inexpensive; accommodation tax is 7% - you collect it from renters and pay it to government; and it's not difficult to comply with minimum standards.
Collecting and remitting the hotel tax is something the BTB is quite serious about.
Check with income tax dept about what is due - in general the tax is 1.25% of your grossincome, but I believe you need to earn above a certain amount before that kicks in.

Thanks, Diane. We'll look into the idea further should we decide to rent it.

to Bettygib, we six Placencia fans will be down Mar 5th and would like to check out your possible rental. Would you mind putting us in touch with someone that could give us directions. We'll be spending some nights at Tradewinds. thanks clint