Ok, after some more experimentation I have a few answers for this in case anyone else is similarly struggling. Apologies to anyone who knows this already but I thought I'd write down my findings in case it's useful for others who like me have yet to find much written down for anything other than the more obvious stuff in the built-in Help features!
To recap, when adding a point-to-point connection on a wiring diagram or similar (where connection points have been properly added and attached to so it is a connection and not just a random line), Visio will try to route it as best it can, which is often not great! Having added it though, its route can be edited, as can that of an already-drawn connection.
To do this all you have to do is make sure the connection in question is highlighted first. If you've just drawn it then it probably will be already, but if not then simply click anywhere on it. You should see dots (like connection points) appear on all the corners and midpoints of all the lines involved in that connection. Move the mouse pointer to any of these, it should change to a 4-pointed cross at a corner or endpoint, or a two-ended arrow for a midpoint, and after a second or two a message should pop up next to it saying either "Adjust Corner", "Move Midpoint" or "Move Endpoint". The message will look like a small square speech bubble. If no dots are visible or no messages pop up then the connection is not properly selected or it's not a real connection. If you're zoomed in for detailed drawings then it sometimes helps to zoom out at this point as the line will reduce in width but the dots won't, making them much more visible.
Assuming the pop-ups appear then you can click and drag them around quite merrily. If you click and drag a midpoint near to an endpoint which is attached to a connection point then Visio will generate an extra couple of corners so as not to disconnect that endpoint.
I'm sure this info must be available elsewhere but I haven't found it yet! Either way I hope it's useful to someone out there :-)