I have learned during my (nearly - on Thursday) 3 years as a research statistician.
1. The hardest thing about any job is learning what questions you need to ask. It's frustrating to not know what you don't know, and I think it's the #1 reason that starting a new job is so stressful. I'm not sure how to learn what questions to ask other than by asking a lot of questions- many of which will ultimately not be the right ones and you will mess things up anyway- and to keep trying and keep taking new projects until you start to see patterns in your work. You'll start to learn what you don't know and how to find the answer.
2. The most important question to ask is "Why?" - Once you can answer this about everything you do, from "Why am I writing this paper?" to "Why am I using this method?" with something other than, "Because my adviser/boss told me to" you are your way to becoming a good researcher. I will call you in 20 years when I've got that down.
3. Never underestimate your ability to mess things up - It is an inevitability. You will transpose two numbers and not catch it any of the 25 times you check that section of your program. You will have to redo your analysis because you didn't control for some mystery variable you've never heard of. You will have to e-mail out a new spreadsheet- and CC all coauthors- when you realize there was one solitary "4" that you didn't change to a "5". Check, double check, triple check. Learn from your mistakes. Be paranoid that you will screw up because you will.
4. This means other people will mess up, too - It is an inevitability. Don't be angry and certainly don't act like you've never done the same thing, because you have. Learn what you can from a situation and move on. Sometimes that means you have to adapt your plans. That's fine. Keep working. Papers and grants don't write themselves while you sit and stew over a mistake someone else made.
5. One year of work experience is worth 5 (at least) in the classroom - Every problem in school comes gift wrapped to you with a label that tells you exactly what it is. This is a categorical data analysis problem. This is an exercise where you use a built-in function to read in a dataset from Excel. Problems in the real world are unclear, messy, and full of hazards. More like What do I do when I just presented my results from an analysis only to find out that one of my numbers doesn't match something on a Powerpoint slide created in 1997 because I didn't control for a variable that I didn't knew existed? or Why won't my program work right now when I needed to give an answer 5 minutes ago? Sure you need an educational background in your subject to learn on the job, but school never teaches you how to handle the most difficult situations you will be faced with in real life.
These are the five things that immediately come to my mind, but I'm sure there are others. What would you add to this list?