Gender is usually not an issue at all; in fact, most native speakers (those who are not concerned with or interested in language issues) are probably not consciously aware of many intricacies of German declination. For example, based on my own personal experience, I bet you that many native speakers are not consciously aware of the frankly insane and deplorable custom to make the adjective declination depend on the definite-ness of the article , as in ein lauter Knall vs. der laute Knall. Most students of the German language, I'm afraid, have to learn and understand these rules.
This unconscious correct usage, typical for native speakers, is true for many other peculiarities, for example distinguishing between male and female subjects when using the possessive pronoun — ihr Auto vs. sein Auto.
But when things become complicated, that is, with constructs not common in everyday language, native speakers start making mistakes. A common example is mit großem, lauten Knall when it would be in fact correct to say lautem1, since all the parallel adjectives are declinated alike. (I suppose that the speakers, including myself, feel a parallel to the correct declination in mit einem lauten Knall mentioned above; the need for an "m" appears to be fulfilled, so to speak.) With a definite or indefinite article, which would be used in casual speech, the problem would not arise, which is why even a native speaker may be unsure here.
And then there are ways of speaking which are mistakes by the standard grammar rules but wouldn't be considered wrong by the speakers or their peers. Dialects, of course, deviate from the standard language, but many variations below the dialect exist within certain groups of speakers: Peter sein Auto instead of Peters Auto is an example that was not uncommon in the suburb of Hannover where I grew up, even if the speakers didn't speak any "official" dialect.
1 Correct at least according to the Gesellschaft für deutsche Sprache e. V. The Duden apparently is inconsistent here, see the discussion with David Vogt below. Historic and probably contemporary uses are mixed in any case, and David has a point that the line between common "mistakes" and common "usage" is permeable and moving.