I got 4 times the "500 Internal Server Error" when updating to 3.7 the following website:
But this one worked good at the first try, however it took around 3 minutes...
Note: this one has got the French version of WordPress
Both are located on the same server.
Below the error message:
Internal Server Error The server encountered an internal error or misconfiguration and was unable to complete your request. Please contact the server administrator at [no address given] to inform them of the time this error occurred, and the actions you performed just before this error. More information about this error may be available in the server error log.