Like any touristy place, rental car break ins are common, particularly at car parks near tourist attractions, but generally only as 'crimes of opportunity' -- as in, it is unwise to leave temptation visibly available. If you keep the car locked and nothing visible in the cabin (like luggage, cameras, a GPS or phones) you will probably never have a problem.
Like-wise, there are 'undesirable' parts to every town/city and even though Ireland is extremely safe, the same applies there. For example, unless you are on the 'Hop-On / Hop Off' Belfast City Tour, you'll have NO compelling reason to visit Falls Road or Fishamble Street (where 99% of all the sectarian violence occurred during the Troubles), as it's not particularly 'touristy' anyway.
There are a few locations in Dublin that I would categorize as 'dodgy', too -- mostly late at night, but nothing that should cause alarm, provided you are reasonably alert and exercise adequate 'street smarts' .
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Bob
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What he said. Keep stuff hidden, don't leave your car looking like a tourist vehicle, and you should be fine anywhere. There are a couple dodgy neighborhoods in any big city, but they aren't were you are likely to end up, such as in Belfast and Dublin. Scams - minor scams involving DCC (Dynamic Currency Conversion) are possible, google that before you go. Nothing huge, but it does happen, and has happened to me a couple times.
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May the light be your guide and the darkness be your comfort!
