How will flying through mountains cause altimeter problems?
You basically answered the question yourself already.
Venturi states: the sum of pressures in a system stays constant.
The system is the valley and the pressures are the air (static pressure) within the valley and the wind flowing through it (dynamic pressure).

Static Pressure + Dynamic Pressure = Total Pressure
If the wind flows faster, we got higher dynamic pressure. Since the sum stays constant the static pressure has to fall as a consequence.
Of course, then, all pressure levels shrink under lower static air pressure as they would do under cold temperatures. Flying at a constant pressure level results in following these shrinking levels and eventually end up at a lower true altitude.
That's the main reason why your true altitude is lower than your indicated.

If you knew the actual static pressure in the valley, you could adapt your altitude by the rule of thumb: per 1hPa: 30ft

So answering your question: if the venturi effect reduces static air pressure in the valley, the above stated applies.