The Tigers have officially extended Brandon Inge's contract through 2012 with a team option for 2013. So, he will continue to be the Tigers starting third basemen for at least the next two years. Inge has batted .230/.314/.394 from 2008-2010 and we can probably expect a similar performance in the future. That is not the kind of production you usually want from a third baseman, but his strength has always been his defense.
Inge is still a plus defender at the hot corner, but does not have the range he had in his prime. Based on three popular range metrics - Defensive Runs Saved (DRS), Ultimate Zone Rating (UZR) and Total Zone (TZ) - shown in the table below, he peaked in 2006-2007. All of the figures are runs saved above the average third baseman. The final column is the average of the three measures. During 2006-2007, he was one of the elite third basemen in baseball. For the past three years, he has been a little better than average.
Table 1: Brandon Inge - Runs Saved Above Average, 2006-2010
He is going to be 34-years old next year, so further regression is likely in the near future. I won't say it's a great move but I don't think they had a lot of options. They have a lot of holes to fill and they won't be able to fill all of them. It will probably be easier to upgrade at designated hitter and corner outfield than in the infield.
Information for this post was gathered from FanGraphs and Baseball-Reference.