The fact you can pick up other channels makes it unlikely that the antenna is your problem. You should be able to hear USCG traffic on Marine Ch. 16 and 22 from their Garibaldi location (Station Tillamook Bay). They are essentially line-of-sight, as there aren't going to be any repeaters. So if you are quite a distance away you may not be receiving them.
Now if you bought the Radio Shack 800 MHz handheld antenna, that could be degrading your reception. It works okay on VHF frequencies (such as what's in Tillamook County), but it isn't the best choice. Also, make sure you don't have your scanner's attenuator feature activated.
I would suggest picking up something like the Diamond RH77 with a right-angle BNC adapter so you can plug it right into the back of your Uniden BCT-8. Total cost maybe around $25-30 at most. Check out Ham Radio Outlet, Amateur Electronic Supply, Scanner Master, or Universal Radio online.
These three things are going to affect your reception:
1. Location/Distance from Transmitter
2. Elevation/Geography
3. Antenna
Good luck -- let us know how it goes!