It's important to realize what intellectually dishonest debate is.

John T. Reed points out that there are only two intellectually-honest debate tactics:

There are only two intellectually-honest debate tactics:

1. pointing out errors or omissions in your opponent’s facts

2. pointing out errors or omissions in your opponent’s logic

The list of intellectually-dishonest debate tactics would be much longer. It's very simple though to remember the two rules above that Mr. Reed mentions.

It is very important to know the difference between honest and dishonest debate. Dishonest debaters, willingly or not, are able to bypass their opponents sense of reason with the many fallacies they use. 

Maybe you know someone who uses a lot of B.S. or dishonesty in their speech. Maybe you don't, or aren't aware of who you speak with or listen to on TV or the radio, or read on the internet, and who is intellectually dishonest.

Much of what is intellectually dishonest isn't blatant lying. It's the rhetoric that goes under the radar and misrepresents facts by embellishment or omission. It could be a faulty line of reason to come to a conclusion. 

Here are some links worth looking into in case you'd like to understand intellectual dishonesty better.

Intellectually-honest and intellectually-dishonest debate tactics
The article that first opened my eyes to the nature of intellectual dishonesty. A really good, easy, read that hit home for me at a time when I was subject to a person who engaged in a high amount of intellectually dishonest rhetoric.
Logical Fallacies Handlist
While I haven't read this completely, it seems to be a field guide to logical fallacies, "Fallacies are statements that might sound reasonable or superficially true but are actually flawed or dishonest."