Miller were quite good but like any large housebuilder they still had sites that were not of good quality.
Part-exchange saves you a lot of hassle and estate agents fees but it is critical you get a fair market price for your old home and are not overpaying on your new one.
As always do you research and DO NOT use Miller's suggested/recommended firm of solicitors whatever they say!
It is illegal for any housebuilder to require you to as a condition of the sale!
Good that you are have the house professionally snagged and inspected, Most of the better older firms are UK-wide. Make sure you have the inspection done before you legally complete.