Line/inbreeding is not a problem in itself. As long as your mice do not carry the same genetic issues there will be no problem. Inbreeding will quickly help you determine if your colony has any genetic predisposition to health problems. For example, you have a doe who carries a gene for tumors and an unrelated male who doesn't. You breed them together, none of the babies have tumors, but some carry the gene for it. You could go a few more generations without having tumors pop up, and then all of a sudden you do, and a good portion of your colony carry it so you could be dealing with this issue for quite a while before you are able to cull it all out. Now lets say you had bred the doe to a brother who also carried the gene for tumors, you would have known probably in the first litter that they had that issue.