Besides the temporary hit on your credit score, there isn't really any downside. However, you may not want to close the account immediately after getting the bonus. The card issuer tends to not look very favorably on that. Keep the card for a year or so and charge something minor to it every few weeks just to make it look like you're using it normally.
If you have any plans to apply for a mortgage or other big-ticket loan in the next few months, I would probably not take the credit score hit. Otherwise, it shouldn't make much difference in the long run for your credit history.
This is actually a pretty run-of-the-mill credit card bonus offer. There are even better ones out there if you spend just a little time researching.