java.lang.ArrayIndexOutOfBoundsException etc

The server crashes with the error java.lang.ArrayIndexOutOfBoundsException and null pointer exception.
Same error occurs on Java 7 SE JRE and OpenJDK 8, both of which are FreeBSD versions.
The crashes appear out of the blue, sometimes very often and sometimes with hours between. A whole day of intensive playing will not mean that the server will crash.
Something that I've noticed a few times is that when the server starts up right after the crash, a cow has died and a piece of raw meat is on the ground. Are the entities are doing something invalid?
The crash reports track it back to different entities.
See crash reports.