What do the molecular orbitals of a single water molecule look like?
First things first, orbitals are not real: neither atomic, nor molecular. Except for, probably, one-electron atoms (also known as hydrogen-like atoms), where one might still argue that to get the orbitals you need to treat the nucleus as a classical point particle that just creates a spherically symmetric electric potential which can be already considered as an approximation. For many-electron systems, one have to necessarily make the so-called mean-field approximation (plus the Born-Oppenheimer approximation prior to that for the case of molecules).

Second, in principle, no further approximation is done in LCAO-MO procedure; it is a purely algebraic trick of expanding a function over a complete set. Such expansion is in principle exact, but the problem is that a complete set is infinite, so in real-world calculations we have to truncate the linear combination at some point which indeed is yet another approximation.

Thirdly, analytical expressions for orbitals are known for one-electron systems only (such as $\ce{H}$ atom, or $\ce{H2+}$ molecular ion) since the electronic Schrödinger equation was solved analytically only for such systems.

And finally, strictly speaking, it is electron density that was imaged with STM, not orbitals. The fact that it closely resembles the density corresponding to orbitals we get in our calculations justifies the quantum chemistry as a whole: at the end of the day, with all the above mentioned approximations we still get something that is close the reality!