Some disadvantages of IP fragmentation are:
A. Once packet is fragmented it can be reassembled only at another end. If there is larger bandwidth on the way, it cannot take an advantage of that.
B. The overhead is large when IP fragmentation is used. IPv4 does not restrict fragmentation and can be performed at any link along the path. This can result in heavy processing demands on the routers in the network. (Not in IPv6).
C. There are some security issues with fragmentation. (e.g. Tiny Fragment Attack and Overlapping Fragment Attack)