So to try and sum things up so far..
Your Windows Mobile 6.1/6.5 device may show SMS messages sent or received after 12:00am 1/1/2010 (local time) being sent or received in the year 2016, when the messages are viewed in Threaded mode. MMS messages seem unaffected.
No fix has been published yet, and although LG and HTC seem to be aware, no official statement has been made. Your carrier's Customer Support resources may not have complete information, and may give you inaccurate or anecdotal info until official word is out.
Devices, regions and carriers affected:
Seemingly any Windows Mobile 6.1 or 6.5 device, any carrier, any region..although it's not completely certain at this point. Positive repros on Touch Pro 2, Touch Pro and Mogul.
See
http://www.howardforums.com/showthread.php?t=1606400, where some non-WinMo LG devices are exhibiting the problem.
Software affected:
Your choice of stock/custom ROM does not seem to change the problem. Mixed reports of SPB Shell and TouchFlo/Sense exhibiting the behavior. Native WinMo messaging software seems to consistently repro.
Reporting additional scenarios (positive or negative)..it's helpful to have specific software versions (OS, TouchFlo/Sense/SPB Shell), custom ROM name and version (if applicable), carrier, country you live in.