what's the impact if I change /var/tmp's permission into 750?

usually /var/tmp area is used by many internal commnads like sort to create internmediate files and its also used by clusters to create some of the log file so be careful while changing the permission.

I have never came across anyone who have changed the perm for /var/tmp

and when it's done anyway, various applications will crash or behave unexpectedly.

yep, it's usually a given for sys admins & various programs that /var/tmp will be writeable/readable to all. Is there a reason you want to change it?

If /var/tmp is chmodded to 1777 (like /tmp) then anyone can write a file to that directory but only the owner of the file can delete that file, a useful way of setting it...

It is actually the default and mandatory way to set it under Solaris.

/var/tmp d none 1777 root sys SUNWcsr