Your preparer may be excellent at US returns, US practice runs on W-2s, 1099s and K-1s, but European banks, funds, pensions and companies issue none of these, so the foreign side of a return is easy to miss.
A return filed without a required Form 3520, 5471, 8621, 8858, 8865 or 8938 stays open past the the seven-year statute of limitations until filed correctly. Most carry penalties from $10,000 per form, per year. Missing FBARs, filed separately with FinCEN, carry their own.
Missed foreign tax credits cut the other way: you paid US tax that European tax should have cancelled. Refund claims stay open ten years.
The fix: amended returns that report everything and claim every credit. Non-willful taxpayers abroad can usually use the Streamlined Foreign Offshore Procedure, which waives the penalties. That door closes once the IRS contacts you.
The additional tax is often nil; the exposure is in the forms. We bring them current.