While there is no additional cost for trading ADR, the institution who sponsors the ADR will charge a periodic fee, not too different than expenses charged by a mutual fund. The difference is the MF expenses are absorbed by the fund share price, while the ADR fees are debited off my account, just like they deposit a dividend but in reverse.
Some examples: for TSM (Taiwan Semiconductor), I was charged $6.81/100 shares last year. For Unilever, $2/year/100 shares, etc...
They also withhold foreign income taxes when depositing your dividends. Foreign government income taxes of course could be high, although you can get some deductions or even tax credits on US taxes to compensate.
"Those Who Can Make You Believe Absurdities Can Make You Commit Atrocities" - Voltaire (1694-1778)