Is there some way of closing programs on Ubuntu-Touch that doesn't involve swiping to the left? I find that I can't reliably close programs using the 'swipe' method.
Just use the powerful sidebar!
You can open the side bar by swiping from the left edge to the right and stop swiping before the middle of the screen.
The side bar contains your favorite apps plus all apps, which are currently opened. The opened apps are marked with a white dot at the left.
Do a long tap to the app you would like to close.
A little menu opens, which lets you choose to close (Quit) that app.
Not unless you are using a device in the converged mode with windowed applicaations, then you can click on a window close button in the title bar area. However, applications which are not in the foreground are paused, and should be automatically killed by the system, if additional memory is required. They may occupy memory in this state, but should not be able to consume any CPU, due to the security restrictions of the system.
It sounds like you may be experiencing a bug that makes it difficult to swipe reliably, in which case you should file a bug report.