Yes there is a problem with the cover matching up with the main breaker. If you or your father can meet with the contractor and explain your concern about a faulty cover he then can have his employee come back to fix the error. You can explain that you would prefer that it be fixed before the inspector "forces" the repair by rejecting the installation. The National Electrical Code does not permit such an installation.
The articles of the 2008 NEC code that apply to this are very clear:
110.27 Guarding of Live Parts.
(A) Live Parts Guarded Against Accidental Contact.
Except as elsewhere required or permitted by this Code, live parts of electrical equipment operating at 50 volts or more shall be guarded against accidental contact by approved enclosures or... (the rest of this article does not apply)
408.38 Panelboard enclosure
Panelboards shall be mounted in cabinets, cutout boxes, or enclosures designed for the purpose and shall be dead-front.
(Dead-front is opposite of live-front, which would be exposed live electrical parts such as you have). There are several other locations in this code that prohibit exposed electrical parts, but these two articles should be sufficient.
If the contractor and the inspector both refuse to remedy the problem, (which unfortunately does happen on rare occasions) you can enclose your pictures in a letter to the chief electrical inspector of your locale asking that the panelboard cover be repaired in a safe and code compliant manner. Be sure to reference the permit number in any correspondence.
As a last resort, you can have a competent licensed electrical contractor repair the panel and sue your contractor in small claims court for the cost, which would be minimal (less than $500.00).
A final note, even a residential home inspection before sale of your home would most likely make note of the unsafe condition of the panel both because of unsafe touch hazard and also because of the possibility of sparks created within the panel from the unlikely event of a short circuit which a properly installed panel should be able to contain.
If the contractor says that the panel was "made that way", tell him to take it out and install one that is not made that way. I have never seen such an installation in 40 years of electrical work.