Highslide JS pretty much pre-dates the advent of mobiles, and just isn't built to handle them. There is a little mobile script that takes care of the worst of the problems by doing things like eliminating the thumbstrip (if you had included one) and by providing different navigation icons, but it was never more than a kludge. You can get it here:
http://misterneutron.com/mobile.js, but I can't vouch for it at all. It's over five years old.
Tablets like the iPad are generally OK, but in phone browsers, things get ugly in a hurry.
For controls, the "text" type of controls are a better choice than the original default "graphic" controls. The targets are easier to hit. Or you could use the fixed controls in the mobile script.
If you pinch to zoom in, you're in no-man's-land. The script simply has no idea that you've done that. It can't react to it, because it never detects it. It knows only about the original size of the browser viewport, before you zoomed in on it.
Highslide JS is abandonware at this stage of the game, so the chances of a rewrite to accommodate newer devices (including things like recognizing swipe gestures) are very, very close to zero.