It's mostly the formulas that lead to misleading reports. The stats are first an estimate, based on incomplete information and informed guesswork. The revisions are made when the raw information is near complete. The informed guesswork is dropped. The revisions are widely reported too.
I don't think there is much gaming on the guesswork side. The real misleading attributes are baked into the methodology of the calculations, and which of those number is reported. There is more than one "unemployment" calculation. But the one that is reported is the most misleading one.
There are hundreds of different CPI stats each month but I believe the one that is reported excludes food and energy as an example.....