Probably the best you can do is extract a list of element ID numbers that were modified after a certain date. That would be a trivial thing that can be done with a simple vba program. Every entity created/copied in a dgn file is given a unique ID number along with a time stamp showing when it was last modified. You would need to locate those elements by their ID numbers in the dgn file to find out what they actually are. Again, this can be done with a simple vba program. Other than selecting the elements in your files, do not manipulate any of the elements or the time stamp will be overwritten with the current date!
HTH...
HTH...