We know that electrons go round the nucleus. But in my textbook, it is written that Rutherford's model was incomplete as the electrons would collide with the nucleus because of Maxwell's law.
But in Bohr's model, the problem remains. Because even in this model the electrons go round the necleus.
So
The question about electrons not crashing into the nucleus is answered is the duplicate here.
To directly answer your questions :
Is Bohr's model incomplete in this sense?
Not even incomplete. It's essentially an empirical rule used to fit the data but without a real basis for it's assumptions. It was, however, a stepping stone to more complete quantum theories.
Is Maxwell's theory incomplete?
Surprisingly yes. Although in a practical sense Maxwell's theory is perfectly usable for real problems, a more complete (or more fundamental, if you prefer) theory of electromagnetic fields was developed called Quantum ElectroDynamics (QED for short).
And it's worth noting that quantum field theories are also incomplete in the sense that we cannot build a working one that incorporates gravity. You never really get a "complete" theory, you get a "good enough" theory that matches what we see and can measure. And that theory becomes "incomplete" when it doesn't fully explain something we see or measure.
There are cases where electrons do crash into the nuclei they orbit, and this is known as electron capture.
Electron capture is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shell.
It is also a method for which some unstable isotopes decay.
