A private key is simply a 256 bit number. Almost any 256 bit number is a valid private key, with the upper limit being slightly less than 2256 due to the order of the secp256k1 curve that bitcoin uses. If your wallet was to generate a 256 bit number above this limit by chance (somewhere in the region of 1 in 300 trillion trillion trillion chance), then as per BIP32 it should simply skip this value and proceed to the next one. The only way it could use an invalid 256 bit number as a private key would be to calculate it as modulo n, (with n being the order of the curve discussed above), which would result in a much smaller 256 number which is a valid key.
Seed phrases are generated from your entropy. Any 12 word seed phrase could be used to generate a seed number, as it is simply the input to the PBKDF2 function, which then generates the seed number for your wallet. However, the final word of standard BIP39 seed phrases contains a checksum for the rest of the phrase. Again, your wallet should automatically generate a valid checksum, but if it didn't, the seed phrase could still be used to generate a wallet while ignoring the invalid checksum.
The short answer is provided you are using an established wallet, then no, you do not have to worry about invalid seed phrases or private keys.