Are there any short or long term effects apparent in tissues if a zone (or the whole) of human body is scanned with ultrasonic waves often?
Ultrasound is considered a safe procedure (reference) which is accepted by the WHO as well (reference). There have been studies however, that show the link of ultrasound treatment to some undesirable traits.
Ultrasound could be possibly linked to a decrease in body weight on birth of infants (reference).
Frequent use of ultrasound may influence babies scanned to grow up left handed (reference)
A significant migration of neurons (change of neurons from their rightful area) has been observed in mice on exposing them to ultrasound at the prenatal stage. (reference).
A study has found detrimental affects to the brains of mice on exposure to ultrasound in the fetal stage (reference).
So based on these papers, I wouldn't call them a 100% safe but these tests all relate to repeated usage of ultrasound imaging. Ultrasound usage sparingly and on valid medical indication should not be a matter of concern.