755/777 Permissions after install?

I know a lot of the directories need 755 or 777 during install but do we need to change these to something like 644 after the install is complete?

Thanks for any advice

All directories 755, all files 644, and no higher. You can use FileZilla Client to right-click the basal directory or directories, reset the permissions box tp 755, then in the checkboxes recurse, into directories only (that'll tell it dirs, subdirs). Rerun ditto but 644 and files only. It'll sail through them. You may need to do directories one at a time unless you can select-all for the 755 run, recurse, directories only. You may need to do basal files as a select-all set for a 644 run, recurse, files only. If you can get below the public root, then you can start with it and take care of everything. No directories should be 777, the 2nd and 3rd 7s are security risks (used to be the way, but not now, the unexpected lesson was learned, some people aren't nice). Each "7" means read-write-execute, and in essence the 1st digit is "owner" (Linux-speak root), the 2nd digit is "group" (system, including Apache), the 3rd digit is "world" (all outsiders), system can obtain "7" from owner as needed as controlled by owner, and "7" does not belong in outsiders' mitts. Your master keys are sevens, your master locks are fives and lower. On many servers 777 is no longer even doable, it's safeguarded against.

If your server has "a problem with that," then it isn't worth the headaches waiting to happen, get another server.

I had to set the vcache and log directory to 777 so I would not get an error. Everything else seems to be working fine.
Any thoughts on these being 777?

755. Vqmod is not specially privileged to require vulnerable 777. If you have one particular .xml that is somehow electronically Medieval, then get rid of it. Slide them aside (into a /vqmod/xml/setaside/ directory, for example) in little groups or onesies till you isolate the culprit(s). After each pass you should flush vqmod's cache (one basal file, the rest in cache/), in order to see the outcome.