If one performs only three rak'aat of tahajjud (total) on most nights, intending to perform witr, and performs no other rak'aat, what is the mistake or problem with this?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

It is permissible to perform three Rak’ahs only at night with the intention of Witr and Tahajjud. The minimum Rak’ahs for Witr is one Rak’ah and the minimum complete performance of Witr is three Rak’ahs.

Tahajjud is the night prayers after having slept.

For more benefit, please refer to Fataawa 83333 and 83303. 

Allaah Knows best.