I worked in that very same business for 6 years - 3 in moulding (injection and blown), 3 in filling.
I don't have a checklist but I can give you the following tips as I remember from the moulding days:
1. Materials! Materials! Materials! Make sure that you use materials that have nothing on any banned cosmetics list.
2. Make sure you have processes for lot traceability to the plastic, colors, and additives. Even regrind in some cases.
3. If there's anything with SPF that they'll be using your parts for you may have to have you parts in an FDA drug master file (Type III for containers) because SPF is classified as drug product http://www.fda.gov/cder/guidance/1714fnl.htm
4. Inspection and test. Depending on the customer they may specific requirements for things other than dimensionals like light transmission through the material, color limits, flash limits, etc.
I found that cosmetic companies are far more picky about the appearance of the part then the actual dimensions.
As I think of more I'll add.