Implications for Artificial Intelligence

None.

Some philosophers have tried to use the Halting Problem as an argument against the possibility of intelligent computers. Stripped to its basics, the argument goes like this:

There are things computers cannot do.
We can do those things.
Therefore, we must be superior to computers.

The first premise is undeniably true.

The second premise is generally supported by displaying a program that solves some subset of the Halting Problem, then describing a clever trick (not incorporated into the program) that solves a slightly larger subset.

There may well be valid arguments against the possibility of artificial intelligence. This is not one of them.