If the compression stroke on the #1 cylinder hits at a location on the distributer cap/button, then someone pulled the distributor at some point and didn't put it back in properly.
The engine can run just fine like that, just starting at the new location for #1 and wiring it in the order that you used the first time.
Use a sharpie to mark the new #1 location on the distributor cap for future reference
As I said, it should run absolutely fine like this as long as the distributor isn't off enough to make setting the timing impossible.
If thats the case, get a new gasket or O ring(if needed) and yank the dist. after getting #1 on top dead center of the compression stroke and reset it so the button points the right way (with the #1 on the cap)
About the wires.. The angle boots on the distributor side of the wires can give you a hard time also, popping out or off when the contact isn't snapped in properly.
My trick on this problem is to put a drop or two of saliva (gotta spit anyways

) on the wire where it enters the boot, then pushing the wire out of the boot about 2".
I then spread the gap on the terminal making it about a 16th of an inch wider.
Snap the terminal into the cap, then slowly work the boot into place.
(Ford has two types of caps, the above is for the older caps with internal connections for the plug wires)
Until I started spreading the gap and installing wires in that fashion, I was always plagued by mystery misses and back fire issues when the terminals lost contact.
You shouldn't have that issue with the externally terminaled caps, but I always squeeze the wire terminals a little tighter to make sure