Drop down menu problem

Is the arrow thing happening in a specific browser maybe?

I think you were on the right track when you said:

'It can happen sometimes when the URL you’re visiting doesn’t match the two URLs set in “Settings > General”.'

I've just realised that the arrows are there if I visit http://www.focusedphotographers.com/ but missing if I visit http://focusedphotographers.com/

My settings say that both the WordPress Address (URL) and Site Address (URL) is http://www.focusedphotographers.com

So I'm not sure whether I should change it. That seems a bit scary in case it messes something up. But at least I've got some sort of explanation now.

That would do it.

You can ask your hosting to do the redirect for you, or you can do it yourself: https://www.siteground.com/kb/how_to_redirect_nonwww_urls_to_www/