What can I do to mitigate this risk?
Make sure the company is solid financially. Talk with the team to make sure you can get along personally with them. And do the best job possible for your new employer.
Make sure the company is solid financially.
You should also do due diligence on your prospective employer. Are their financials solid? What is general outlook for the company and their industry? It has been my experience that more people are let go because of financial pressure than because of any job performance related issues. If you are risk adverse avoid going to any company that does not have a solid financial picture or that is in an industry is having difficulty. Right now construction and mining equipment manufacturers are having tough times, and the healthcare industry is still in a state of turbulence. I would avoid these sectors today but that could change in a few months.
Talk with the team to make sure you can get along personally with them.
The second leading cause for dismissal is a bad culture fit. People who come in and do not mesh will with the company culture cause problems for managers. This is rarely the official reason for letting someone go but it is the underlying cause of the decision. I have seen many people who were incompetent at their job but were able to fit in with the team and work well with others that were kept around. While "superstars" that were great at their duties but did not mesh well with the team were let go. The reason is that a whole team working well together can usually outperform a team of "Superstars" that work at cross purposes.
For this reason I really like the all day interview. I find out more about my perceived fit with the new team at the lunch than I do most of the morning. I find lunch is the best opportunity to bond on a personal level with the team, and find out if we are a good fit. Anyone can get along for an extended lunch, so what I am looking for is common interests outside work. If you do not find those shared interests or if you think that one or two people on the team may be a little to much for you, then I would consider how badly you really want to switch jobs. Especially if you have a position you enjoy now where you feel secure. I have found that most of the time my opinion of the team that was formed at a lunch is confirmed over time. There are rare exceptions of people who are very different in the interview than they are when actually working, but I would not count on that.
Do the best job possible for your new employer
Employers generally do not hire someone with the intention of letting them go right away. There are of course exceptions but for the most part your position should be safe if you do what is expected.