snopal has pointed you towards using or instead of || because the former is a lower-precedence equivalent of the latter. Another way to solve your problem would be to use parentheses with your open so the || doesn't bind the file name and the flag together.

open(FILE, ">test.txt") || $failed_flag = 1;
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It is often recommended these days to use the three-argument form of open with lexical filehandles, like this.

open my $testFH, '>', 'test.txt' or $failed_flag = 1;
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Cheers,

JohnGG

Update: I really must learn to type faster :(