If you're staying for a few days, choose the weekend to go to Murano/Burano etc and get off the main island or you'll be forced to shuffle along the alleys with thousands of others.
It's tedious and you get bumped and trodden on. Definitely stay away at the weekend if you have children as they'll be bumped and trodden on, albeit quite unintentionally.
The police are very good and you'll often find them stationed on the narrower bridges getting everyone to try and cross in some sort of civilized order.
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At Least Do This: If you can't avoid the weekend at carnival time be up and about early and once you're stuck in the hoardes, be patient. The most annoying thing is people pushing and shoving you out of the way. We're all trying to get around and pushing doesn't help and people get angry.
Alternative: I try to do my trips away from the island on the weekend so get a boat out to Murano, Burano or Torcello or Isola San Michel.
If you have to stay on the island, visit the less touristy areas. Remember, the further away you get from St Marks Square, the quieter it will become.