iron the wrinkles out (of/in something)

1. Literally, to remove wrinkles from something, especially a piece of fabric, using a flatiron. Your new dress shirt is all rumpled! You'll need to iron the wrinkles out before you go to the ceremony this evening. I have to iron out the wrinkles in this tablecloth before our guests arrive. I'm sure the hotel has an iron, but I hate having to iron the wrinkles out of my clothes on vacation.

2. By extension, to ease, solve, or remove minor difficulties, troubles, or problematic details (of or in something). (Sometimes worded as "some wrinkles," "a few wrinkles," etc.) Our latest software update is nearly finished—we just need to iron a few wrinkles out before it's ready for release. Your friends and family are great means of support when you need to iron the wrinkles out in your life. Bob and Janet are seeing a counselor to try and iron some wrinkles out of their marriage.