Originally I posted this information here: http://forums.androidcentral.com/moto-360/471939-what-do-when-360-misbehaves.html in the 360.1 forum. I think it probably applies just as well to the 360.2 (which I also now own) so I am posting it here too, slightly altered for the new model.
Here is a procedure to try when you are having problems with your 360 such as:
1) Poor battery life (unless your device is new, remember that it can take a number of charge/discharge cycles for new batteries to reach their ultimate capacity) (A normal 46mm model battery should last at LEAST 16 hours per charge with light use, and always-on screen on and tilt-to-wake also on. It will last at least a few DAYS or longer with the always-on screen turned off and tilt-to-wake also off. The 42mm model has a considerably smaller battery, so always-on screen with tilt-to-wake might not last a normal waking day's use, even if that use is light.)
2) Lag (strange pauses that don't seem normal)
3) Mysterious behavior (like crashing, freezing/locking up, flickering screen)
4) Missing notifications
5) Inability to maintain consistent connection to the phone, even though it is very close.
Before trying this procedure, of course try rebooting the watch and/or phone, since that requires far less effort and can often fix minor issues. (You can also stop after step 1 and see if there is any difference before continuing).
1) Uninstall any and all Wear watch apps you installed from the phone (but do NOT uninstall Android Wear, itself) THEN
2) Wipe the cache for the Android Wear app on the phone (settings-> apps-> Android Wear-> Force Stop, then Clear Data, then Clear Cache) THEN
3) Remove Android Wear from your phone completely THEN
4) Factory wipe the watch (on the 360, Settings-> Reset Device) THEN
5) Reload Wear on the phone THEN
6) Pair the two THEN
7) Try it completely stock this way for days and see how it goes. Do not change any Wear settings or install any watch apps or faces during your test period (unless you want to change the always-on screen or tilt-to-wake options to match what you are used to).
If your problem was only battery life and the above did not fix it, then try turning off the "tilt to wake" function which can only be accessed from your phone under settings while in the Wear app. If this does fix your problem, then you might be accidentally waking the watch constantly with certain movements and you should just leave tilt to wake off (you then wake the watch by touching the screen or pressing the button). Some people just wake the watch more than others do, so it can be hard to compare life with others with that tilt-to-wake setting turned on (which by factory default, is on).
Otherwise, if your problems persist, the above are the most drastic "cure all" so you might have a hardware issue and your only recourse is warranty/replace. If it passes the tests OK over the next days, then carefully add single apps or settings changes, one or few at a time, to see what happens over additional days, so you can narrow it down what you did that caused the original issue.
Here is a procedure to try when you are having problems with your 360 such as:
1) Poor battery life (unless your device is new, remember that it can take a number of charge/discharge cycles for new batteries to reach their ultimate capacity) (A normal 46mm model battery should last at LEAST 16 hours per charge with light use, and always-on screen on and tilt-to-wake also on. It will last at least a few DAYS or longer with the always-on screen turned off and tilt-to-wake also off. The 42mm model has a considerably smaller battery, so always-on screen with tilt-to-wake might not last a normal waking day's use, even if that use is light.)
2) Lag (strange pauses that don't seem normal)
3) Mysterious behavior (like crashing, freezing/locking up, flickering screen)
4) Missing notifications
5) Inability to maintain consistent connection to the phone, even though it is very close.
Before trying this procedure, of course try rebooting the watch and/or phone, since that requires far less effort and can often fix minor issues. (You can also stop after step 1 and see if there is any difference before continuing).
1) Uninstall any and all Wear watch apps you installed from the phone (but do NOT uninstall Android Wear, itself) THEN
2) Wipe the cache for the Android Wear app on the phone (settings-> apps-> Android Wear-> Force Stop, then Clear Data, then Clear Cache) THEN
3) Remove Android Wear from your phone completely THEN
4) Factory wipe the watch (on the 360, Settings-> Reset Device) THEN
5) Reload Wear on the phone THEN
6) Pair the two THEN
7) Try it completely stock this way for days and see how it goes. Do not change any Wear settings or install any watch apps or faces during your test period (unless you want to change the always-on screen or tilt-to-wake options to match what you are used to).
If your problem was only battery life and the above did not fix it, then try turning off the "tilt to wake" function which can only be accessed from your phone under settings while in the Wear app. If this does fix your problem, then you might be accidentally waking the watch constantly with certain movements and you should just leave tilt to wake off (you then wake the watch by touching the screen or pressing the button). Some people just wake the watch more than others do, so it can be hard to compare life with others with that tilt-to-wake setting turned on (which by factory default, is on).
Otherwise, if your problems persist, the above are the most drastic "cure all" so you might have a hardware issue and your only recourse is warranty/replace. If it passes the tests OK over the next days, then carefully add single apps or settings changes, one or few at a time, to see what happens over additional days, so you can narrow it down what you did that caused the original issue.