We were always allowed to use our FastPasses even after their stated times, too. Not a problem once.
Another bit of advice I have is that if you have some in your party who don't want to ride certain rides, but others in your party REALLY want to do those rides, go ahead and get FastPasses for the entire group. I don't do roller coasters, and my mom sometimes did and sometimes didn't, but my daughter and dad really loved them -- so a lot of times we'd get fastpasses for the entire family but then I'd chicken out and they'd go twice, using the FPs, while mom and I took my toddler on something more our speed or just gave him a rest break.
Alternatively, you could split them up -- ie, get FastPasses with part of the group's tickets for one coaster, and then FastPasses for another coaster with the remaining tickets, and then the thrill ride nuts could ride 2 coasters while the rest of the party did something tamer.
In general, I found that relatively few of the rides I really enjoyed required FP's, so I was quite often happy to let other members of my family use my FP's.
Finally, if you don't use all of your FP's, don't let them just go to waste -- you can always pass them along to someone waiting in the regular line. We looked for families with small children that looked like they were getting worn out. Passing along the Disney magic is a great way to make someone's day -- and yours
Other tips: have each person carry a water bottle on a strap or in a beltpack, or maybe have a group backpack (which you take turns carrying) with water bottles in it. Keeping hydrated is essential. Take along ponchos, too, because afternoon showers are to be expected, and you can always use them on wet rides as well. If nothing else, you can wrap your shoes in them so you're not walking around in squishy shoes after the ride
Finally, lots of people recommend a break in the middle of the day, but if you're hot and tired but don't really want to leave yet, try to find a nice air-conditioned show and then grab a snack before or after it. It can really go a long way toward rejuvenating you!