There are several issues that I have noted with the new LDS Irish records site. I had just come back from a short trip to Dublin when the Irish GRO data went on line so knew the format of the index books and what I was looking for.
First, do not select any "event" before going into the site. These seem to have been provided for church register data and not linked to this data base and so no results appear when they are selected (I seem to remember that the first few days they were linked but very inconsistent). The same applies to dates as it seems to be very inconsistent in how it treats them.
You can refine by event, approximate date, etc. once you are in the database.
Otherwise, do use both a first name and a family name (and even the general district, if you are sure of it). Make sure you select the district from the drop-down list as even if you enter it exactly the same it won't recognise it and will say no results.
The database is a bit flexible in handling variations and will find a given name even if it does not occur first in the entry (e.g. Jane will also find Mary Jane). It's also very slow as it's Flash-based and not cross-linked for marriages, and not possible to select by mother's maiden name even for those entries that have this (later than in the rest of the British Isles, but that's due to the indexes being prepared that way). The date selections are also only in 10-year blocks, not a problem with less common names but a real nuisance with more frequent ones.
There seems to be a problem that if there are too many matching entries, there will be NO error message but it will only give you the first few thousand results, so that further refinements will be within only a partial set of results. Obviously, if the name you want is unusual, you can omit the district and select that just when you refine your search.
There also seem to be some issues in that entries already on IGI don't seem to be there - maybe because they got lower priority as more data (from the full register entries) was already out there, so remember to check both.