I generally use the BRCGS Food Standard as a guide to these things, and it pretty much breaks this down into site approval for the supplier/manufacture sites and risk assessment of the material to cover risks including:
• allergen contamination
• foreign-body risks
• microbiological contamination
• chemical contamination
• variety or species cross-contamination
• substitution or fraud (see clause 5.4.2)
• any risks associated with raw materials which are subject to legislative control.
You also haver to make sure any approved changes to raw materials including primary packaging are communicated to your goods-intake function - which is particularly important for pre-printed packaging.
As a couple of pointers, the most clearly defined risks to consider are chemical hazards defined by legislation. You can reference this source of EU legislation: Legislation (europa.eu)
In general, a migration analysis is a good way to demonstrate compliance here, but keep in mind that different categories of foods have different thresholds for migration based on fat or ethanol content - so you need to link this back to your HACCP
to make sure you're drawing the right conclusions.
Similarly, when it comes to microbiological risks, you'll need to risk-assess contact packaging materials based on your product characteristics and the storage and handling conditions - so if you have a retail product presented in a plastic container that the consumer will ultimately cook the food in at home in the oven, your risk assessment would be different to a thaw-and-serve product presented in a paper bag, for example.
My personal experience is that packaging suppliers can react with confusion when confronted with these risk assessments because they don't always understand the relevance of questions over allergens etc. That said, you can come into risk assessment outcomes that you might not always anticipate - I once worked for a food manufacturer that produced gluten-free products packed into a plastic bag in cardboard carton format. The risk assessment of the cardboard cartons revealed that the adhesive used in the manufacture of the cardboard cartons was wheat starch - with gluten present. Further investigation showed that the possibility of migration of the gluten from the cardboard packaging was so remote that the gluten-free claim was still valid, but it's important to thoroughly investigate these things.