Several users who recently updated their device to Android 6.0 Marshmallow, have been complaining about random force close errors with Google Play services, while installing certain Gapps packages for Google's newest mobile operating system. It is ascertained that the Google Play services error is triggered by some permissions issue along the lines of recent Facebook chat heads problem.
XDA recognized contributor, aclegg2011, has recently shared a simple fix to resolve this problem on your Android device, after installing the Marshmallow update.
Fix Google Play Services force close error with Android 6.0 Marshmallow Gapps
Step 1: Download the Marshmallow Gapps shared by Benzo
Step 2: Flash the Gapps after flashing the ROM as you would do normally via TWRP or CWM recovery. Reboot your device and soon you will start seeing Google Play Services errors flash on the screen during the setup. Just ignore the error messages, and proceed with the setup wizard. Finally, the Google home screen should appear on your smartphone's display. When you launch any Google app or use anything that requires Play services, you might get a couple of errors.
Step 3: Let us fix those now. Go to Settings > Apps. Click on the three dots menu button on top right and select Show system.
Step 4: Now, tap on Google Play services app, and then select permissions.
Step 5: Turn on all the permissions. Check if is turned on by default, and if it isn't, just enable all permissions for Google Play services to function smoothly.
Step 6: Go back and exit the settings menu. Go ahead and re-download or reinstall Google apps and the Google Play Services error should no longer appear on your device's screen.