Some questions to ask:
What is the expected uptime, and how does downtime affect your business? What sort of service level agreement can you get, what are the penalties for missing it, and how confident are you that the SLA uptime goals will be met? (They may be better or worse at keeping the systems up than you are.)
How sensitive is the data you're proposing to put into the cloud? Again, we get into the questions of how secure the provider promises to be, what the contractual penalties and indemnities are, and how confident you are that the provider will live up to the agreement. Further, there may be external requirements. If you deal with health-related data in the US, you are subject to very strict requirements. If you deal with credit card data, you also have responsibilities (contractual, not legal).
How easy will it be to back out of the arrangement, should service not be what was expected, or if you find a better deal elsewhere? This includes not only getting your data back, but also some version of the applications you've been using. Consider the possibilities of your provider going bankrupt (Amazon isn't going to go bankrupt any time soon, but they could split off a cloud provider which could then go bankrupt), or having an internal reorganization. Bear in mind that a company in serious trouble may not be able to live up to your expectations of service.
How much independence are you going to have? Are you going to be running their software or software you pick? How easy will it be to reconfigure?
What is the pricing scheme? Is it possible for the bills to hit unacceptable levels without adequate warning?
What is the disaster plan? Ideally, it's running your software on servers in a different location from where the disaster hit.
What does your legal department (or retained corporate attorney) think of the contract? Is there a dispute resolution mechanism, and, if so, is it fair to you?
Finally, what do you expect to get out of moving to the cloud? What are you willing to pay? What can you compromise on, and what do you need?