Blade, Continental's policy (even on a unrestricted coach ticket) is no upgrades unless you're elite. But, as many of the posts in various forums have indicated, you might have luck in upgrading the day of departure if you get the right ticket agent. Try 2 hours before at the ticket counter or an hour before at the gate. If you get a nice agent and first class isn't all that full you might just get it! If you have a good number of miles and segments already this year on Continental, the agent might see that and realize it would be a good thing to do to keep you as a loyal customer.
Good Luck!
Todd