Depends if the area of the loose connection got burned/melted/deformed.
Depends on what the city inspector thinks.
Some electricians will not attempt to analyze (extra cost to you pass or fail) let alone make the repair on old equipment already showing problems.
The lug you have circled in red does look like it got burned on the inside.
Loose connections can develop tremendous heat even well below the rated amperage.
If you have one loose connection and the equipment is many years old, it is uncertain whether there are other places where connections are corroding or oxidizing which can give the same effects as loose connections in the near future if not already loose from some materials expanding as they corrode.
Many panels have parts riveted or welded together so what seems like a small part that got damaged cannot be replaced easily.
The lug is not at the same level as the other. If the lugs are bolted on, you can replace it. Higher quality panel manufactures sell the bus bars, and all other parts as replacements. Not sure how old that panel is.
There may be nothing at all wrong with it. Not sure where you are located. If you can, you can pull the meter and check all the lugs and connections. After that, you will be able to determine what is needed.
I see the top right 2-pole breaker is off. Maybe some more are turned off that are on that lame leg, especially if you had a good electrician look at it. It could be the lug has burned out and ruined the bus bar. Probably better to replace the panel rather than risk a questionable repair that could damage something even more expensive than the panel.
It's good that you caught this before summer when the a/c would be needing full voltage and might get fried or at least tramatized trying to start.
It looks like a Gould panel which is obsolete but parts are still available.
A close up shows what appears the right connection to be properly seated. The left one may be making good contact, but it is sitting too high and is not tightened properly. As the others have mentioned, the only way you can work on it is for the power company to pull the meter. The caveat with that is, you will have to get an inspection by the AHJ before they will reconnect it.
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