How hard is it for bitcoin to switch mining algortihms?
They would need to
hard fork it. This would never get community consensus though. Think the miners are going to agree to make their ASICS immediately obsolete? (Or forced to mine another SHA256 coin, like BCH.) The only way this is going to fly is if it is discovered the SHA256d algorithm has a vulnerability or commuting power increases to such an extent that solving it becomes trivial.
Actually there was a discussion on dev-mailing-list just a while back on introducing an "intermediate" block using different PoW via soft fork. So pretty much everything can be done via soft fork.
There was a discussion on changing block size via soft fork, yep, no need to hard fork to change block size. There was even a discussion on shortening block interval to have much faster blocks for BTC, via soft fork too, written by none other than Vitalik himself. But getting those soft forks to activate via miners or even users would be quite a challenge though....