From an accessibility point of view, if you rely purely on colour coding, the information provided by those colours ('verified', 'problem' and 'unclassified') may be inaccessible (or misleading) to people who are unable to perceive the differences between those colours, either because they are colourblind or are perhaps completely blind. It also makes the information inaccessible to a fully sighted user if they wish to print a black and while copy.
Also, colour coding is an abstracted way of providing information. It's great if the meaning is clear but it only makes sense once you have memorised what the colours represent or if you cross-reference against a key or other instructions. Providing that information explicitly in a column in the table removes that abstraction.
In addition to the colour coding, I would provide that information explicitly within the table, either in text or with an intuitive icon. That would also allow you to maintain the 'click on the column header' sorting method that you describe.