Odds of Getting In
Finding a paleontology job will take more than just blind luck. Each year, you've got bunches of freshly degreed paleontologists trying to claw their way into some sort of paid employment. The key is to make yourself more marketable so you can float to the top of the pile. First, you won't make it by just skating by in your classes; devote some effort and your odds will improve. Your adviser can probably help you land some internships or work/study gigs, as these arrangements show employers you're not afraid of real-world challenges. In fact, some employers might even list an internship as a job requirement.
You'll probably find more job openings in industry-based research, and in university settings, than you will in museums that fund research work. Don't overlook teaching at the high school or junior college level, as these jobs offer the predictability of classroom work with few research requirements. In fact, you'll probably find that junior colleges lead the pack when it comes to new teaching jobs. Just think: You could get paid for helping to launch a new generation of paleontologists.