No, it's not going to be a "bigger" problem down the road. It won't change anything on your tax return. You would basically be sending them a Form 1040-X with no changes and an explanation that you were amended to report that your rolled over your retirement plan, that was reported on Form 1099-R as a direct rollover.
If you do file an amended return, you can download a fillable Form 1040X and fill it out based on the prior amended return. Provide the explanation and mail it in with a copy of the 1099-R. Same thing you will do if you wait for a letter.
The timeline for the IRS to send a letter? If you owe, or are due a refund, usually within a year, but up to two years after filing isn't strange. If you haven't heard from them by now, you probably aren't going to. They aren't going to recoup a single dollar. Of course, the IRS has had some very strange timelines lately.
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