The main danger is ending up with the copper pad/track parting from the pcb.
Yes, I've had that happen with cheaper, low quality PCBs. I had to put the lead of the new component through, then scratch a bit of the lacquer off the trace with a scalpel further away from the now missing solder pad, bend the lead over and solder it to the newly exposed trace away from the hole.
With better quality PCBs the traces are much thicker copper and pad goes through the board:
Another thing to bear in mind is the age of the item. You should be all right with older stuff as they used decent lead solder, which has a lower melting point than modern ROHS compliant lead free solder. With newer stuff I've had trouble melting the solder and I could really do with a hotter soldering iron. When re-soldering I use some WBT silver solder, which is lead based, has a low melting point, flows really well, is easy to work with and leaves nice smooth, shiny joints.