I believe that this will cause your history ordering to go a bit wonky. Hitting up to get the last item will almost always get the command you last typed into the current window (as it should be, imo), but if you hit enter a few times after you run a given command it will be something else (sucked in from the surroundings I guess)
Every so often this really bites me, but the usefulness far outstrips the quirks.
Considering the number of shells I have open, that would be very weird. A coherent "local" history is very useful not just for the up key but also for referring to history items by number (like "!123").
My solution for my laptop has helped me on countless occasions. I've been doing this for about three years.
1. Compile bash with the syslogger patch. Each command will generate one line with timestamp, username, terminal PID, and command.
2. Configure syslog to pipe all bash commands to a special file.
3. Run a cronjob every night that takes all the bash commands from the day and saves them off to a day specific file.
4. Need to find that command you ran 6 months ago to get package XYZ to work in way ABC? Use "grep -R" to find every single invocation you ever made to that program. If you actually needs a particular shell's local history, pipe grep through a grep for the PID (I find I almost never need that).
I work with so many different technologies for such brief times that this is just absolutely invaluable. It also helps you narrow down dates of events sometimes.
Every so often this really bites me, but the usefulness far outstrips the quirks.