An 'inconvenient fact' is a fact that would be difficult for an investigator to refute without their fallacious arguments becoming obvious and making them look stupid.
To overcome an inconvenient fact an LGO investigator often ignores it. Hence they will usually use a combination of fallacious arguments (see my previous four postings for examples) and ignored facts to achieve a finding of no maladministration when they are confronted with a act of maladministration they prefer to bury.
The most common method used by LGO investigators is to break a complaint down into its constituent parts. Then using various fallacious arguments they chip away at these until the only thing left are the 'inconvenient facts'. All they do then is ignore these and reconstitute the complaint using the fallacy of composition and the straw man fallacy. Hey-presto a complaint that will give them the outcome they want.
To make it more difficult for complainants to understand what they have done they will often use further fallacious arguments such as 'arumentum verbosium' and 'Ignoratio Elenchi, that's bags of waffle with a red herring thrown in for good measure to you and me.