Working on my '69 Super Bee restoration.  There are two holes (one on each side).  One is under the battery tray and the other is in the same spot on the other side of the car.  Would I run into problems if I close these holes permanently?  I looked at another car and it appears to have these wholes closed but there are screws holding it in place.  (I took pictures, but I don't think I can include them in this post)  

Is the one on the passenger's side for the battery tray support bracket, or is that already there?  

No, it isn't a part of the battery tray support bracket.  It is like a hole in the engine compartment that provides access to something.  It is closed off on my other car with screws.  I was thinking about welding some sheet metal over it on the one I am working on now.  I just wanted to check to make sure I wasn't restricting access to something by closing it.  

Now I got it. They sound like the alignment access holes used by alignment shops to align the front end. You COULD weld them shut, but I bet the alignment guy wouldn't be happy the next time you take it in.  

Humm....that is what I was afraid of....Can the car be aligned if they are welded shut?  I'm guessing they will have to remove the wheels to do it.  My reason for the follow up question, rust has taken it's toll on one side, so we were thinking about cutting it out and replacing it without the hole on one side and closing it on the other.  I'll check with the alignment shop I'll be taking it to as well.  

It can be aligned without the holes, but your alignment guy will not be happy. It's almost impossible to align a car without the wheels/tires in place.