I have written an app (AutoWifiSwitch) and one of the features I plan to add is automatically disabling the wifi scanning service in my app if power saving mode is enabled.<
This answer is only for the Samsung power saver mode, since as usual Samsung still chooses to mess with the standard APIs.
iKeirNez posted an excellent answer that confirmed a suspicion of mine. This still happens on lower end devices you can buy that have 5.1.1. I have a list compiled of the devices which I know of that suffer from a camera crash when on power saving mode, but I have not yet checked for all the possible keys that relate to power saving mode.
I know about these ones so far:
content://settings/system/powersaving_switch
content://settings/system/psm_switch
You can register a ContentResolver and listen for changes OR you can check it when necessary:
final String result = Settings.System.getString(getContentResolver(), "psm_switch");
Log.v("Debug", "Powersaving active: " + TextUtils.equals(result, "1"));