I usually do the calculation of 1 multi-entry is (roughly) the financial equivalent of 4 (rather than 3) single-entry. So, since it is unlikely that I will travel outside Thailand more than 4 times in a year, I do the single-entry permit and I get it at the airport. It takes about 10-15 minutes and I am always at least 2 or more hours early, it's not a big deal. That also means when I go to CW for my yearly extension, I don't get any re-entry permit there.
It worked for me once but not the next time. I think I used the same browser (though I am not certain) and I did it within the requisite time frame and filled out the online form the same way.
I can add one tip for those from the USA. When I had earlier filled out the form and it didn't work (it went into lala land when I clicked the button to submit the form), I had entered "United States" in the nationality but I had to fight it to do so. It turns out that on this one form out of all others I had entered, it uses "America" which is best selected from the drop list.
I just read the Tod Daniels post referenced above and the other posts in this thread. I have an OA visa and am on an extension and I do not have multi-entry as was indicated. That is a separately purchased item from immigration. Because I make few trips abroad, I get a single re-entry stamp at the airport before leaving. The cost of the multi-entry is about the same as four single-entry stamps so, since I travel only one or two times a year outside the kingdom, the single-entry works for me.