Hardly one to fault others, thaddeus surprised his colleagues when he began even their most trivial mistakes.

caviling at  

Explanation:

The word "caviling" means making unnecessary objections or complaints. In order words it means to raise trivial and irritating objections.

In the context, hardly anyone blamed others for their deeds. But Thaddeus astonished his coworkers  or colleagues when he began to cavil at or make objection at their most unimportant mistakes.

Hence the answer is -- "caviling at".

uhh idk for sure but i think it makes it difficult to pump the oil through the oil rigs

where is the rest of the question. this isn't making sense. can you upload a picture of the question?