The auditor will see that you have omitted part of the key images.
The auditor can see all the outputs received by your account. Without the spend key, the auditor cannot generate the key images corresponding to those, however. In order to prove your balance, you generate a signed list of key images (see https://github.com/monero-project/bitmonero/pull/928 for the new commands and RPC calls to do this,
soon to be merged now merged), and send this to your auditor.
The signatures are essentially a 0-mixin ring signature. Since these have only one public key attached, this proves that the key image is that of the public key.
The auditor then loads those key images, and checks that each purported key image matches the public key of the output that the auditor knows was received. If the signature checks out, it is proof that the key image really is the key image for this output. The auditor can then check the blockchain to see whether this key image appears on it (spent) or not (unspent).
For reasons of simplicity, this check is done in blockchain order, so you're supposed to give the key images in the same order as their appearance on the blockchain. If you omit a key image (or add one, or change one), the signature will not check out, and the auditor knows you're trying to pull a fast one (or, you never know, a bug somewhere, data corruption in transfer, but Questions Will Be Asked).
A special case happens at the end of the list, since it's very possible that new outputs will be received between the time the signed key images are generated and the time they are checked. This is handled simply by stating that the balance is correct as of the last seen block height in the key images (technically, it's also valid till the block preceding the next output received, if any).
As for omitting transactions, this system works on key images for the outputs received. Transactions are not used, so you can't omit any.