Midas alleges that Chadwick, which is now in liquidation, underestimated the amount of steel needed for an IT building at the college within the drawings.
It alleges that 263 tonnes of steel were needed for the scheme rather than 88 tonnes suggested in the original drawings.
Midas also accuses Chadwick of providing poor drainage design that had to be rejected and redesigned.
Further complaints contained in the writ were that the firm failed to send the detailed design drawings in time, and that this led to the project finishing 12 weeks late, that Chadwick failed to prepare the drawings properly.
The result of this, according to Midas, was that it was paid £3.8m by the college but that the total costs it incurred amounted to £4.2m.
Midas claims in the writ that if it had been properly advised, it would have submitted a revised tender that would probably have been rejected by the college and the losses would therefore have been avoided.