I have just "completed" constructing and gluing together my supply side sprinkler manifold. It is leaking at two of the joints. Is there anything I can do aside from rebuilding it from scratch to stop the leaking?
From a plumbing standpoint, no.
The joint must seal from the inside of the joint.
Patching the outside is a waste of time.
If you're using PVC fittings with purple primer and pvc glue, then you won't be out much time or money.
As plumbers, we have all run into that sometime in our career.
For threaded connections, some use Teflon tape, (carefull with this or the strands of it can float through your valves.)
or you can use a Teflon based paste sealant marked for for use on plastics.
I rarely ever use tape.