Water Heater Gas B-Vent Install
Based on the International Residential code (which may or may not apply where you live), this installation is not compliant. Things that I see that need to be corrected include (but may not be limited to):


The vent must be held at least one inch away from wood and other combustibles. 
The total rise of the vent must be at least five feet, to insure proper drafting.
The vent must be sloped so that water/condensate will flow towards the appliance, by at least 1/4 inch per foot.
Screws must be short enough that they do not pierce the inner metal of the vent.
The length of the horizontal section (defined as sections at less than 45 degrees) must be less than 75% of the total rise.
The vent cap outside must be a "type B" cap.
Don't use tape because it would burn. Any small gaps should be OK since the exhaust will pull extra air into the vent, instead of letting the exhaust into the room.


Also, I see that one of the corrugated copper water tubes is a little flattened. You may want to replace it. Also, I see the plastic dielectric at the end of the tube on the right, but not on the left. If there is not any plastic dielectric, I'd suggest replacing it with a tube that has a dielectric. These connections do NOT need plumber's tape or dope. Also, these corrugated tubes should be replaced when the water heater is replaced.