Make sure that your interviewer isn't playing you around, because they absolutely can and will if it only benefits them.
If it's possible, check with someone in the department you are applying for in the atmosphere of that department. The company does not give out references except for the factual report of when you worked there. Within the company, you can move departments, but in that case the supervisor can be asked for reference.
Ask questions about the training. Have them tell you that there is a 70% minimum score you must get on all tests and that you will be fired if you do not achieve this or take too long to achieve it.
Express any concerns you have about having the training all done online. Your trainer will not not always be available for you and no body is allowed to just sit with you to guide you through anything.