I've seen people clean up duplicates from their PATH variable using awk and something like this:
PATH=$(echoprintf "%s" "$PATH" | awk -v RS=':' -v'!a[$1]++ ORS=":"{ if (NR > 1) printf RS; printf $1 }'!a[$1]++') You could try adding that to your own bashrc and make sure you source the other files somewhere before running that.
An alternative would be to use the pathmeargepathmerge utility.
As for your speed problem, this will not affect the startup time of the shell in any significant way but it may save some time doing tab completion for commands, especially when the command is not found in the path and it does repeated searches through the same folders looking for it.
A note on security: You should really heed Gilles' warnings about security here. By sourcing a file owned by another user you are giving a free pass to those users to execute their own code as your user every time you start a shell. If you don't trust those users with your password, you shouldn't be sourcing their shell files.