The author of Exim believes that it is Y2K-compliant, as long as the underlying operating system and C library are. Exim does not parse dates or times at all. Internally, it makes some use of binary timestamps in Unix format (number of seconds since 1-Jan-1970) and uses C library services to convert these to printing forms (e.g. for logging). The printing forms all use 4-digit years.
It should be noted that exim, in common with all GNU licensed software, does not come with any form of warrenty - see the NOTICE and LICENSE files within the distribution. If you need a full Y2K audit performing, then the source is available for this to be done.
January 2000 - its still working, no problem reports :-)