I had a deck where my creatures had lifelink and an exponentially increasing number of +1/+1 counters, and my opponent had Herald of Eternal Dawn preventing him from losing the game, even with negative life. So we got to a point where my creatures had literally billions of +1/+1 counters, and I noticed 2 bugs related to integer overflow:

• The display of life total seems to be vulnerable to integer overflow. After my creatures with lifelink dealt about 3 billion damage to my opponent, my life total was displayed as negative and his was displayed as positive. The life total itself seems to be fine though, I didn't lose, and when I finally destroyed my opponent's Herald of Eternal Dawn he lost as expected.
• Owlbear Shepherd's ability seems to be vulnerable to integer overflow. I had about 300 creatures on the battlefield with a power of over a billion each, but Owlbear Shepherd's ability didn't trigger.

Number of +1/+1 counters and number of creatures don't seem to be vulnerable however. The number of +1/+1 counters seems to be capped to a bit over a billion, and the number of identical tokens seems to be capped to 250 (I had Anim Pakal which was supposed to create a billion tokens since he had a billion +1/+1 counters, but it only created 250 tokens).