What will happen when the time field wraps around I was rather surprised when I read about the bitcoin's block header time field is only 32 bit. Even if it is unsigned (it is) it only get us 68 more years than the Y2K38 problem. What will happen then, will we need to change the protocol? Can we? What would it imply then?

Why at first Satoshi did not put a 64 bit timestamp at first was that intended?
2^32 seconds is 136 years. So, this will become a problem in the year 2106. However, even at that point, there are things that we can do to fix the problem. 

While it is technically correct that the block number is not encoded in each block header, the block number can easily be inferred. Each block header has the hash of the previous block header. If you follow this back far enough, you'll get to the genesis block. You don't even need to download the entire transaction history, just the block headers.

Okay, so we've got the block number, and the date field. Now, we make a rule that on block 4786000 and all later blocks (which will land at about 2100) the date field will be interpreted to be 100 years later. Block 4786000 will state a date of 2000, but because we made this rule well in advance (we did make it well in advance, right?) all of the clients will know that the date actually means 2100.

Thus, we have bought ourselves another 100 years. On block 9572000, we can do exactly the same thing.