Anybody can spend these outputs by simply providing "OP_TRUE <fake_sig>" to the above redeem script.

The flaws in the script are:
- Using OP_CHECKSIG instead of OP_CHECKSIGVERIFY
When you use OP_CHECKSIG it will push the result of the verification to the stack when immediately after your OP_IF is going to pop an item from the stack which is the result of the signature verification. If it is false it won't even execute the branch under it which can be abused by passing a fake signature so that OP_CHECKSIG pushes OP_FALSE to the stack ergo the OP_IF that pops OP_FALSE is skipped.