He is considered very mobile for his size and is also very strong. He is known for his physical presence, being suspended for striking Geelong star Cameron Ling in just his second game.
In Round 14 2008, with the Bulldogs playing Port Adelaide in their annual game in Darwin, Minson was involved in a confrontation with Kane Cornes, a Port Adelaide midfielder. Minson appeared two days later in an interview with the Foxtel AFL program On the Couch, apologising for a derogatory comment made to Cornes. The actual comment is said to have concerned or been directed towards Kane's newborn son who has suffered from health problems, and in particular questioning Kane's priorities in choosing to play football in Darwin that weekend, rather than being back in Adelaide in support of his wife and son. Minson claimed that what was said was in "the heat of battle". 
In Round 12 2012, following the Western Bulldogs victory over Port Adelaide, Minson was again embroiled in a controversy over allegedly sledging Danyle Pearce, another Port Adelaide player. The comments, which are said to have concerned Pearce's mother, were made in the final quarter of the match, immediately after the two were wrestling at a stoppage and during a subsequent melee. Whilst the incident was not elevated to the AFL tribunal, the Western Bulldogs fined Minson and imposed a one-week suspension on him as punishment for the indiscretion. Because of the prior incident with Kane Cornes, a media frenzy ensued. In a press conference two days after the game, Minson said he was "deeply regretful for any comments that were made", and that he had "no intention of ever putting anyone through that again".
Off the field, Minson is known for his intelligence and multi-faceted abilities - he plays saxophone, speaks fluent German and is currently studying civil engineering at the University of Melbourne. He is also heavily involved with the charity Red Dust, which operates sporting and lifestyle clinics in remote aboriginal communities and, more recently, in very poor areas of India.