Car hire can be a cheap and really convenient way of getting around Zanzibar. What you probably need to be aware of before deciding to hire a car is the following:

You will be best hiring a four wheel drive and be aware that all vehicles for hire are fairly old so don't be expecting a newish vehicle but found the rental cost  reflected this. Petrol is also very cheap.

There are a lot of police checks but as long as you have the right documentation to hand it shouldn't be a real problem, although the old fashioned non photo bearing licence might cause some confusion.

Once out of Stone town the traffic is not a real problem and roads not that busy but there is some mad driving, particularly the buses and taxis. 

The maps you are given are not very detailed and the road signs are very hit and miss. Be prepared to get lost but that can add to the adventure.

There are some main roads but be prepared to drive on unmade and rough tracks as most hotels are located away from the main roads, with the exception of some of the 5 star places.  

The locals are very helpful in resolving issues like flat batteries.

Overall despite some of the negatives hiring a car is worth considering.