Let's say on one side of the dumbbell I got 12 pounds, and on other I got 16 pounds. (I got dumbbells with 2 extra weights of 4 pounds...)
Is it bad to add those 2 extra weights to 2 dumbbells on one of their sides?
Sounds like a variation of unilateral work. The important aspect of unilateral work, or uneven loading, is that you switch hands and perform the same amount of work with the other side.
Let's say you are doing shoulder presses with those weights. You'll want to make sure of the following:
So if your goal is 3 sets of 8, you will end up doing 6 sets of 8. First set the left hand has the heavy dumbbell, the second set the right has the heavy dumbbell.
In the end, it's preferable to do true unilateral work than use uneven loading.
If the dumbbell has uneven weight at each end, the applications are a bit more limited. It can work for exercises like hammer curls, but presses of any sort may be thrown off.
Any exercise where the orientation of the dumbbell is perpendicular to the floor should be mostly unaffected (total weight of the dumbbell is pulling the same).
Any exercise where the orientation of the dumbbell is parallel with the floor will be affected (total weight of the dumbbell is pulling differently). This can affect balance issues, and potentially put more strain on your joints that wouldn't be there with a balanced dumbbell.
I wouldn't advise you to exercise like that. Even if you switch hands on each set it will still be uncertain what results you will get out of it.
The only proper solution to your problem would be to use only one dumbbell during your workout. Go for one hand at a time and then do the other. For the first 2 years of my training I had only one dumbbell at home before I started going to the gym and that's how I would workout. Yes it would take a little bit more time to finish a workout but there won't be any negative side effects.
Yes, you can. It is called Offset Loading, and you can read more about it on T-Nation
In summary (direct from the article linked above):