Also, shell aliases and user functions may cause problems.   Though preserving them could also be used as a means of attack.

Actually, the alias and function security vulnerability would be negligible considering that someone can always walk up to a sudo root user's terminal and redefine sudo itself just as easily.  
   sudo()
   {
       /usr/bin/sudo $*
       /usr/bin/sudo evil command
   }
 But this info isn't easy to get outside the shell without modifications.  One approach is to have them be special sudo commands.
   sudo alias ls=ls -lF
   sudo function() { blah; blah }
To some extent, you may be able to use sudo inside of functions.

Another problem was:
   sudo gui-program &
The sudo password prompt didn't appear until program was foregrounded with fg and then it had to be suspended with ^Z and backgrounded with bg.

Due to the temporary use of the defective editor gedit (emacs wasn't installed yet) which doesn't autosave by default, I did have to attempt recovery of commands from sudo.log.    Of course, the logging botched wildcards.    

But here is a perl incantation to convert sudo.log into a useful format for system administration logging. The first perl undoes sudo's line wrapping.   The second one prints just the command field (preceeded by 'sudo ') and intersperses 'cd' commands when the directory changes.

cat sudo.log | perl -n -e '$oldline=""; while(<>) { chomp; $newline=$_; if(substr($newline, 1,1) eq " ") { $oldline=$oldline . substr($newline, 3) } else {print $oldline, "\n"; $oldline=$newline} } ' | perl -n -e 'while(<>) { chomp; ($date1,$date2,$date3, $user, $tty, $pwd, $targetuser, $command) = split(/:|;/); $pwd=~s/ *PWD=//; if($lastpwd ne $pwd) {$lastpwd=$pwd; print "cd ",$pwd,"\n"} $command =~ s/ *COMMAND=//; print "sudo ", $command,"\n" }'

Or for syslog:
(zcat /var/log/auth.log.1.gz; cat /var/log/auth.log.0 /var/log/auth.log) | fgrep sudo | perl -n -e 'while(<>) { chomp; ($date1,$date2,$date3, $user, $tty, $pwd, $targetuser, $command) = split(/:|;/); $pwd=~s/ *PWD=//; if($lastpwd ne $pwd) {$lastpwd=$pwd; print "cd ",$pwd,"\n"} $command =~ s/ *COMMAND=//; print "sudo ", $command,"\n" }'


This doesn't strip out the pathnames for applications found on the path.

But information about weird copy commands was logged poorly:
   mkdir /home/whitis/new_dot_files/
   cp -rp /home/whitis/.[a-zA-Z]* /home/whitis/new_dot_files/
   cp -rp /olddrive/home/whitis/.[a-zA-Z]* /home/whitis
   cp -rp /olddrive/home/whitis/* /home/whitis/
sudo didn't have access to the wildcards.   Yet oddly, when similar commands were done for root, they were logged - because the shell couldn't read /root/ to replace the wildcards.   And the command was logged correctly but failed.   But it worked when done like this:
   sudo bash -c 'echo /root/.[a-zA-Z]*'
so, that is a workaround if you aren't already using nested quotes and aren't using shell variable substitution.

sudo does more or less the right thing if you do something like:
   sudo printf "foo\nbar\n"
   sudo printf 'foo\n$$bar\n'
Except it loses the quotes.   Which in the second case is the wrong thing as the logged command does not have the same effect as the original.

Integration with some sort of emacs (or other editor) client that would automatically append the command executed (and a cd command if the directory changed), to an emacs buffer containing a specified logfile would be great.   Unfortunately, emacsclient isn't that sophisticated.
   editortool --append --open /root/captains-log "tar zxvf /dist/package.tar.gz"
This is a specific case of the general case of executing an arbitrary program specified in /etc/sudoers after each sudo (or admindo) command.

Information on logging, in general:
http://www.freelabs.com/~whitis/linux/captains-log/

It should be noted that some of these problems were due to the mistaken decision long ago to have the shell handle wildcards instead of handling them in a command line parsing library - which would have been just as easy though it would make the programs slightly larger in those days (no shared libraries).   A decision that has been a constant annoyance ever since because things which aren't filenames are butchered unless quoted.

With the implementation of many of these changes, sudo could be a invaluable tool rather than one which is usually used for the wrong reasons (illusion of security and illusion of logging).