Yes, face masks should not only be changed between patients but they should also be changed anytime they become wet.

The Centers for Disease Control and Prevention's (CDC) Infection Control Guidelines for Dental 
Healthcare Settings states the following:

A surgical mask protects against microorganisms generated by the wearer, with >95% bacterial filtration efficiency, and also protects DHCP from large-particle droplet spatter that might contain bloodborne pathogens or other infectious microorganisms. The mask's outer surface can become contaminated with infectious droplets from spray of oral fluids or from touching the mask with contaminated fingers. Also, when a mask becomes wet from exhaled moist air, the resistance to airflow through the mask increases, causing more airflow to pass around edges of the mask. If the mask becomes wet, it should be changed between patients or even during patient treatment, when possible. (1)

1. Wear a surgical mask and eye protection with solid side shields or a face shield to protect 
mucous membranes of the eyes, nose, and mouth during procedures likely to generate 
splashing or spattering of blood or other body fluids (IB, IC). (1)
2. Change masks between patients or during patient treatment if the mask becomes wet (IB). (1)

In addition, the authors of Infection Control & Management of Hazardous Materials for the Dental Team state that the mask should be changed with every patient because its outer surface becomes contaminated with droplets from sprays of oral fluids from the previous patient or from touching the mask with saliva coated fingers. Also, when a mask becomes wet from moist exhaled air, the resistance to airflow through the mask increases, causing more unfiltered air to pass by the edges of the mask. Thus one should replace wet masks to maintain high filterability. (2)

Resources:

1) Centers for Disease Control and Prevention's (CDC) Infection Control Guidelines for Dental 
Healthcare Settings:

http://www.cdc.gov/mmwr/preview/mmwrhtml/rr5217a1.htm

2) Infection Control & Management of Hazardous Materials for the Dental Team. Third Edition. 
By Miller and Palenik. Elsevier/Mosby Publishers. Copyright 2005.