1. Complexity: Implementing CTV and designing smart contracts that leverage its capabilities can be complex. This complexity could lead to bugs or vulnerabilities if not done carefully.

2. Increased transaction sizes: Using CTV often involves creating transactions with many inputs and outputs, including decoys. This can result in larger transaction sizes, which may lead to higher transaction fees.

3. Limited adoption: The privacy benefits of CTV are maximized when many people are using it. If adoption is limited, the anonymity set may be smaller, making it easier to trace transactions.

4. Regulatory concerns: The enhanced privacy features of CTV could attract regulatory scrutiny, as governments and law enforcement may be concerned about potential use for illicit activities.

5. Fungibility concerns: If CTV transactions stand out from regular transactions due to their distinctive structure, it could potentially harm Bitcoin's fungibility if they are treated differently by exchanges or other entities.

6. Wallet support: CTV requires specialized wallet software that can handle the creation and signing of covenant transactions. Not all wallets may support this functionality, limiting accessibility for some users.

7. Irreversibility: If a mistake is made in a CTV contract, such as sending funds to the wrong covenant address, it may be impossible to recover the funds since the spending conditions are enforced by the contract.