Can you cite three or four gaffs radio and TV newspeople (or commentators and actors) make all the time?

Yes, indeed. I notice all the time such errors such as:

"The convicted criminal was hung by the neck until dead." (Nope, he was HANGED by the neck until dead.)

"This bacterium was found to be the cause of the outbreak." (Nope, a STRAIN OF BACTERIA was found to be the cause.)

Mispronunciation of the word "often." (The "t" is silent.)

Incidentally, the other responder should have referred to a mistaking of "objective and accusative cases." That was a good example of how people will overcorrect in attempting to speak in an educated way (and end up sounding foolish).

I think you mean "gaffes". A "gaff" is an iron hook with a handle for landing large fish. ... But then you ask for examples of grammatical errors, which are different from gaffes, so I'll address the latter request:

One common mistake is commentators saying "irregardless" which is a redundant form of "regardless".

A second common grammatical error I've heard a lot on Republican radio is a commentator referencing the Democratic Party as the "Democrat Party".

A third frequent grammatical violation of news commentators and others: use of the subjective case (in a sentence) when the objective case should be used.

For ex: "She launched the ball toward Mary and me." becomes "She launched the book toward Mary and I."

ETA: Wrong, grammatical errors are not automatically considered "gaffes" (or "gaffs" as you like to spell them). Also, to whomever "thumbs downed" this, kindly provide justification. Thanks.

Thunder gave decent examples. Lots of actors and singers put on fake english accents at award shows like Madonna who pretends to be english.