Ok, my turn.
Restrictions in promoting the products. For example some Networks/Merchants only allow English sites. Or maybe you are not allowed to promote competitive products, or maybe you are not allowed to promote them on forums, etc. Fail to comply with the restrictions and you will lose your commissions or even get your account canceled.
Payment methods for the affiliate commission. It's trivial, but if a Merchant only makes Paypal payments to their affiliates, and the affiliate can't have a Paypal account - well is not good for the business
Complaints research. You are not going to get a commission if the order turns in a refund or chargeback. A light research to check if there are a lot of complaints about the products can be a good idea.
And another one for software sales:
Trial Version. If you are to promote a software product, it would be very good to find out if they have trial versions - far more easy to promote a thing when you have actually tested it
)