Yes you can. One or two people have had an issue with older versions of Safari on iPhones but I use an iPhone and have no problem with doing this now. And in my experience Safari is a lousy browser anyway! I do not believe we have had any reports of problems with Android based phones - at least I do not remember any.

I would start by trying a different browser and if that doesn't help then there is probably a script conflict with the mobile side of your website. That can happen depending on the Wp theme or other plugins abiding by the WP API and rules but can, sadly, be really hard to find... although you can use a browser like Chrome on your desktop and run it in mobile mode to test things.

Only removing components one at a time, clearing the browser cache and then trying in between each item removed remembering that the culprit might be your WP theme. Although you can connect an iPhone to a desktop version of Safari (Mac) and use the script console on the desktop to interrogate what is happing ion the phone.