Young Harold Finch's father says that the engine is flooding. The part he holds up is the accelerator pump diaphragm. This could not cause flooding. This part causes fuel to squirt into the throttle body when the accelerator is depressed. If anything a torn diaphragm like that would cause a lean condition when starting, not flooding. It would also cause a hesitation.
Shaw says that Claypool has Top Secret Clearance or better, which is not possible. Top Secret as the name denotes is the highest clearance. With Top Secret Clearance there are other additions one can hold which includes sensitive compartmentalized information, white house clearance, nuclear secrets, etc, but they are all based on Top Secret Clearance.
Claypool is being guarded by the Secret Service, but they only guard the president and his family, former presidents and their spouses, foreign leaders in the US, or others upon an executive order. Since Claypool was in the National Security Agency, their agents would most likely provide security although other federal law enforcement agents could be designated such as the US Marshals, FBI, and possibly even military law enforcement as the NSA is considered a military agency.
The flashback when Harold is helping his dad is 1969. However, the date code on the carburetor is 4 digits. Holley used 3 digit date codes in 1969.