You may want to take a look at Gary Katz's book "The Doorhangers Handbook" (available through amazon, most bookstores, etc...)It covers everything to do with installing doors. I've installed a number of prehung doors (both singles and double/french doors) on the remodel that I'm doing and would guess that in your situation it might be that while the jamb sides are plumb and square to the top jamb, the actual hinge side jamb is slightly "twisted" when compared to the latch side jamb. In other words, when looking straight at the hinge side jamb the side of the jamb with the hinge on it is pulled in more than the other causing it to twist. This will cause the door to not close properly. To test this, try taking a crowbar or something and prying the hinge side jamb out a little - probably around the middle hinge and see if it seems to close better.

Sorry if this is a bit confusing but asuming the jambs are not bowed, the door is flat - not warped, square, and the hinges are set properly somehow the jambs are not aligned right. They only have to be off a tiny bit to throw things off. Good luck to you!

"The Doorhangers Handbook" is out of print, but it looks like he put out a new book, "Installing and Hanging Doors" just a few years ago. Same size, so I assume it's very similar. I'll look into that.

You may be right about the hinge jamb being twisted. Haven't had a chance to look at it today, but I'll take some measurements. I'm thinking that the bottom part is twisted in. That would explain why the door is flush at the bottom of the latch jamb ant not the top, and why there is almost no gap at the base of the hinge jamb.

When I nailed in the jamb, I didn't have the slab attached. I thought this would make it easier to shimb the jamb and work with everything. Now I'm wondering if maybe not having the weight of the door on the jamb might have affected it. None of the instructions I've seen in Lowes/Home Depot or online really break out the steps, so I was taking a guess at that. Any thoughts on what is the best way to go?

I've always hung doors with the slab out - then made adjustments after installing the slab. As I mentioned, if you've just nailed the jambs in (as opposed to screws) you should be able to shift the jamb slightly with a crow bar to get a final fit. I should also mention that in my case the molding was not on yet and I was using solid jambs vs. split jambs. When all looked good I then put in some screws behind the hinge plates (can't see them then.) If the jamb is secured, even just with nails, and shimmed properly the weight of the door, whether it is wood, solid core, or hollow shouldn't make a difference. If it's a very heavy door over time it may sag a little if not properly attached or the house settles or the hinges give a little but not as soon as you hang it. My guess is that the jamb is a bit twisted and with a little adjustment all will be well.

Do you have a 6 foot level?
If you do you can check hinge alignement and that the the jamb is vertical on the face and also not tilted away formthe face of teh wallby checking the edge. Plumb needs to be checked in both planes.
Squares are notoriously bad for door use. A 24 inch level is better. If the side jambs are vertical and the top level then the jamb is square.
If it is warped it should easily show also.
IF you have both 6 foot and 24 inch levels, check them against each other for straightness. It is not perfect but you should be able to see any serious bends. You can also check them against a string and a plumb-bob, but it can be hard to see very small errors.

No 6 foot level, just a 4 foot and 2 foot. Wasn't able to find the 6 foot at Home Depot or Lowes, still looking.

Nevertheless, I have made some improvement by adding additional shims behind the hinge jamb, as well as putting in nails both in front and behind the door stop. The slab is now pretty much level, not sagging, and the gap between it and the top jamb is almost constant. Have a couple tight spots along the hinge jamb, but when I add some more nails, I know that they will go away. And I started nailing the latch side, and I know I can get that just right.

So with all that in place, I checked the jambs in every way possible with the level. They are plumb and level, no issues at all, but the top of the slab on the latch side still sticks out by nearly a half-inch. Turns out the slab is warped, just a little. It's fine at the hinge side, and is flat at the bottom of the latch side, but I can see it's no longer level at the top of that side. I guess I bought a defective door, and I'm betting the other door I tried to install has the same issue.

All this has gotten me pretty upset at Curtis Lumber. They have a number of stores in the area, but four of six closet doors were scratched, two of the pre-hung doors were chipped, and now at least one of the pre-hung slabs is warped. I haven't even checked three of the doors or any of the trim I bought. I thought supporting the local business would be a better bet than the national chain, but now I'm regretting the decision.

For door hanging you really need a 6 foot level. It is long enough to span the hinges and check the entire jamb for straight and plumb.
If you had placed a 6 foot on the door slab you probably would have seen the warping instantly.
The Johnson brand aluminum levels are a decent price and quality.

Door frames have to be plumbed on two planes---done by putting the level on the door stop as the door closes on it---as if the level is the door---- and then parallel to the door---so the door can be closed with the level in place.

Another advantage is to use finish screws instead of nails. The act of nailing will compress the shim pack, causing the jamb to bow. Using a finish screw---the heads are not much larger than an 8 penny nail---allows you to 'adjust' that bowing effect.

Walls can be out of line enough to cause the door slab to seem to warp in referrence to the jambs. Another issue is the way the hinges are mortised into the door/jamb. Cheak those very closely. If that problem exists on every door, it could be door construction related.

There are times when a wall is so far off line, I have to shim the jamb trim out from the wall to allow the door slab to close evenly.

I installed an apprehend door and when I close it , light come in at the bottom

Here (<-- link) is a link to Gary Katz door installation video. I used that technique/ sequence on interior doors at my son's house and it worked well. Basically, Gary makes sure that the framing isn't "cross legged" and then provides the steps to install the door so that it's plumb in BOTH directions then provides a sequence for fastening.