First, you should put all of your repair requests in writing. This creates a record of your complaints, and gives your landlord an indication that you are serious about addressing the landlord's responsibility to make necessary repairs. A landlord does have the responsibility to make necessary repairs, and if the failure to make these repairs make the apartment unlivable, you would have grounds to terminate the lease. The failure of the landlord to return phone calls would not really be sufficient to terminate the lease.
Second, you should check with your local state and local building code officials to see if any of the repairs needed violate any housing codes. If so, you can let your landlord know that your housing code official has been contacted. You can check the following to see if there might be a violation: New Hampshire Housing Codes Healthy Homes Provisions.
In terms of the dog hair situation, a lot would depend on whether you were aware at the time you entered into the lease whether or not you knew there were dogs in the premises, whether you informed your landlord of your son's allergies, and whether there was any agreement between the parties that there would not be any dogs or dog hair problems. By itself, I don't really believe you would be able to use your son's allergies to dog hair as a grounds to terminate the lease unless there was some agreement with the landlord that there would not be any dogs or dog hair.
Another option is the possibility of withholding your rent in order to get the landlord to make repairs if the mechanical issues are serious enough. Withholding rent must be done carefully and should be properly documented. You should read: A Tenant's Right to Withhold Rent.
Given that this a temporary 4 month lease situation, there is the possibility that you simply move out. But this should only be done if you give the landlord a notice of termination of the lease if he fails to make necessary repairs within a reasonable period of time. Since this lease is only for four months. At worst you could only be held liable for 4 months of rent ( or 3 if you have paid the first month) if your termination of the lease is found to be improper by a court.
The primary thing you should be concerned about is fully documenting in writing the repair issues, your complaints in writing to the landlord, and a notice of termination of lease if warranted if the landlord continues to make necessary repairs.