We use a simple shell script like the one below. You'd, obviously, have to tweak it somewhat to tell it about the different file names and decide which box to look for which on but you get the basic idea. In our case we are tailing a file at the same location on multiple boxes. This requires ssh authentication via stored keys instead of typing in passwords.
#!/bin/bash
FILE=$1
for box in box1.foo.com box2.foo.com box3.foo.com box4.foo.com; do
ssh $box tail -f $FILE &
done