Do I have any legal recourse against a shoddy contractor?

Pursuant to MCL 570.1114 a "contractor does not have a right to a construction lien on the interest of an owner or lessee in a residential structure unless the contractor has provided an improvement to the residential structure pursuant to a written contract between the owner or lessee and the contractor and any amendments or additions to the contract are also in writing."

As such, if there was no written contract a lien should have not been placed upon your house. You should be aware that pursuant to MCL 570.1117 the holder of the construction lien must foreclose upon the lien within one (1) year from the date that it was recorded. As such, if the lien has not been foreclosed on within one (1) year after it was recorded you can file an affidavit with the register of deeds to have the lien removed. MCL 570.1128 provides:

If any statement or claim of lien has been recorded in the office of a register of deeds, and the time within which proceedings to enforce the lien through foreclosure has elapsed without commencement of the proceedings, a person with an interest in the real property affected by the lien, or that person's agent or attorney, may make and present to the county clerk of the county in which the statement or claim of lien was recorded, an affidavit showing the time when the statement or claim of lien was recorded and the names of the parties to the statement or claim of lien. The county clerk shall examine the records of his or her office, and if it appears that proceedings to enforce the lien have not been commenced with the time provided by law, the county clerk shall execute and deliver to the owner a certificate of that fact, bearing the seal of the circuit court. The certificate may be recorded in the office of the register of deeds for the county where the statement or claim of lien was recorded, after which the statement or claim of lien shall have no effect.

Alternatively, you can file an action to quiet title and may receive attorney fees pursuant to the Michigan Construction Lien Act as the lien should have never been filed without having a written contract.

Finally, you can file a complaint with the Michigan Department of Energy Labor and Economic Growth if the contractor was licensed as it appears the contractor violated the Michigan Construction Lien Act by placing a lien on your home and by doing poor work.