First vintage Omega : Ref 166.0163

I just received my first vintage Omega watch. (Ref 166.1063, with the cal 1012 movement). Has a bit of patina and probably has seen a polish (considering how faint the logo is on the back) but nothing too bad for a watch I paid 260 USD. Crystal isn't original, nor is the strap. Serial suggest the end of 1974, which seems correct.

Seems to be keeping good time (around +4s/day, timed with my iPhone). However, after the first hours, the date function didn't work (it didn't pass from the 9th to the 10th). It has been working fine since (it passed from the 10th to the 11th fine, and so on). Is that something I should worry about? The quickset feature works well. The seller is offering me a refund, but if this isn't too big of an issue or just normal after winding the watch the first day, I'd like to keep it.

First thing you do when you receive a watch you want to wear, you get it serviced. If you can tell us where you are, we can suggest somewhere to do that.

I am from Montreal (Quebec, Canada)