Here is a listing of when to go to the doctor:
The wound is jagged.
The wound is on your face.
The edges of the cut gape open.
The cut has dirt in it that won't come out.
The cut becomes tender or inflamed.
The cut drains a thick, creamy, grayish fluid.
You start to run a temperature over 100°F.
The area around the wound feels numb.
You can't move comfortably.
Red streaks form near the wound.
It's a puncture wound or a deep cut and you haven't had a tetanus shot in the past 5 years.
The cut bleeds in spurts, blood soaks through the bandage or the bleeding doesn't stop after 10 minutes of firm, direct pressure.
Here is a neat scouting site about stitches, including information about how long is too long for stitches.http://www.glenn.cockwell.com/scouting/Stitch.html
It looks like 24 hours is the maximum. However, he does say that knife cuts are less likely to demand stitches than jagged cuts. The main reasons for needing stitches are scar minimizing and infection prevention. My take is that your dh can't get stitches anymore, but he should do all he can to minimize the chance of infection and to bring the edges of the cut together.
(Only if he has full movement of the joint of course).