Odds of Getting In
The good news is that jobs for oceanographers are growing faster than the national average (source). One reason for this is that there's more of a concern with how the environment affects people and how we affect the environment. Research facilities, universities, corporations, and the government are all in a hiring frenzy, looking for the brightest minds to help them examine and solve this 21st-century problem.
This means there's going to be more and more of a need for smart people to come up with policies, both for conservation and for the extraction of needed resources. That means you should have a polished résumé and a fair amount of good references. We're just saying, with the job market already ready to bring you aboard, you'd better not give companies a reason not to hire you.