Signatures insert HTML into messages. Poorly formatted signatures insert bad HTML into messages and could cause a variety of problems.
Here are some tips on how to debug issues with signatures:
1) Ensure that the signature settings are correct in Options > Preferences > Accounts > [your accounts] > Identity. This panel drives how and where the signature is being placed.
2) Use Quote Mode instead of Summarize until you have your signatures working as expected. Summarize dynamically constructs the HTML for digest view in outbound messages, and during troubleshooting, this variable should be eliminated from the equation.
3) As a test, try creating the simplest signature possible, just one line of text with no formatting. Does the simple signature work, whereas the other signature does not? If yes, then this could indicate an issue with the other signature(s).
4) Ensure your signature HTML is correct by clicking on the </> button in the Signature editor.
5) Do NOT insert an image into a signature that is behind your secure corporate firewall! It will not work, and it could prevent messages from sending.