Since you asked, here is my opinion. The major impact is not on your local client traffic but the remote services being provided by the Internet.
Dynamic Fragmentation should NOT be enabled due to several reasons. One of which is fragmented packets are now used for denial-of-service attacks. Also, they can be used in circumventing firewalls and intrusion detection/prevention systems allowing malicious code to be sent through. Fragmentation also places an ever increasing burden on network elements and applications to fragment, resemble, and buffer these packets as well as increased overhead for retransmission of lost/dropped packets. Furthermore, more and more techniques are being utilized on the Internet to secure communications from client to server. So, having the router tamper with the packet by fragmenting it up into various pieces could break these types of secured communications without a application level gateway (ALG) being developed such as the PPTP and IPSec (VPN) ones the DIR-827 has. In short, it is not worth enabling the dynamic fragmentation option because it is out-of-date and can silently and adversely impact communications.