You can use find to skip unwanted files, no need to grepafterwards:
find PATH \( -name '._*' -prune \) -o -type f -iname '*.mov' -execdir echo {} \;
To create a text file with the result, add > path/to/text-file at the end.
PS: The reason your second command doesn't work is in the pattern used for grep. You strip out the path name in the find, so grep -v '^\._' should be used instead.