I haven't run in to any issues. What version of Google Play and Google Play Services do you have?
I just got updates from the Apps app, I think yesterday. My app settings show the following versions:
Google Play Services: 23.06.15
Google Play Store: 34.5.10-21
If you have versions that are way behind these two, then I'd suggest you update via the Apps app, make sure Google Play Store is installed, and if Google Play Store is asking to update either itself or Google Play Services allow it to do so.