Cons:

• Light - Projectors hate light. If a projector had to pick between going to dinner with light or with Kyle Whittingham, it would pick Kyle, every single time. If you want a good picture you need a dark room. 
• Screen - You need a decent screen to get a good picture. No a white wall isn't ok, but some DIY screen builds aren't too terible
• Bulb life - bulbs last 3000-5000 hours or so depending on the projector and then you need to replace them $$)
• On/Off - Frequently turning the projector on/off reduces bulb life. Best if you use it in larger blocks of time. 
• Sound - Sound has to go through a separate audio device, like a stereo
• Source - No built in tuners. You want to watch tv, you'll need a device (DirecTV, Dish, Roku, Blu-ray, etc) to get the picture to the projector. 
• Placement - They can be tricky to place. It depends on your screen size, ceiling height, specific projector, etc.
• Noise - projectors run hot and need fans to actively cool them. They tend to be noisy. Where your pojector is placed relative to your seating will directly impact how noisy it is while viewing. 

Pros:

• Really, really big screen. You feel bad for people that only have an 80" tv. 
• A good quality projector paired with a nice sound system the closest you can get to a theater experience at home.