there can always be problems but as long as the contingencies are the only justification you would intend to use to invalidate the contract, it sounds like you should be fine.
one contingency not in what you provided would be any necessary financing. If you have not included anything regarding such, if you cannot find financing and do require such, you are still on the line to purchase the car or be subject to whatever penalties a breach would allow.
as I said, there can alway be problems and there are many more possible problems you have not addressed but, it is hard to address every one.

