Many of them use a two-digit field to store dates. This could cause problems. Time billing, accounting, spreadsheet files, and many database applications fall into this category. The actual problems depend on how the programs handle their two-digit dates. Many of them assume the first two digits are 19.
Some programs have a more complex method of dealing with the date.
For dates ranging from 00-49, Lotus will represent the years as being from 2000 to 2049. Making life more miserable is the fact that many programs will handle things differently from version to version. It is important to track which versions of any application you are running and strive for consistency because using multiple versions of these applications concurrently and sharing data among the versions may cause unpredictable results. Many of these can be managed at the application level by upgrading the application that creates the files. However many companies have database and spreadsheet files that have been created over the years and are used internally for many different purposes.