Please update to the latest version of Firefox, version 37.

Updated Firefox to the latest version (v37) and it does seem better however, it still isn't 100%. Tried duckduckgo for instance and a long press didn't work. Oddly, if I visit a link on the page and hit the back button once it's loaded, long pressing nearly always starts working.

Be default in search pages the link will open up in a new tab. However in duckduckgo I could tap on a search title with an underline and it would open in the open search tab. Is there another example where we can test this consistently?

Unfortunately, I am not able to find a page where this consistantly happens it seems intermittent on any web site I've visited. Yahoo today seems particularly bad. I have updated firefox again (to v37.0.2) and it still happens.

I'm not sure what a search engine automatically opening a link in a new tab has to do with anything, that shouldn't stop the pop-up menu appearing when you long press a link.