I have just read “Can I make cabinet doors out of plywood?”, I was thinking of making some doors out of mdf with mdf strips glued to the front so they look like they have a frame.
Am I going to get problems?
You shouldn't have any problems using MDF.
A lot of modern cabinets are made out of MDF these days as it's a cheap material to use. It comes in a variety of thicknesses so you'll be able to get one that meets your requirements.
You need to wear a mask when cutting and sanding it as the dust is not very nice.
It takes paint well and you should have no problem gluing strips to the face to give it some depth and character.
I would not use MDF in an area with lots of moisture like a bathroom or a garage. It will swell up and degrade quickly if it gets wet. If you do use it in a wet area seal it up well.
Cut edges of MDF tend to not be very attractive... kind of "rough". You can buy special high build primer/surfacer to smooth it. Or buy "Rangerboard", a type of MDF which has a better quality core.