How does the range of orbit tilts impact astronomers search for transiting exoplanets?

The transit method of detecting exoplanets looks for slight changes of star's luminosity as a planet passes between the star and an observer. That means that the star's orbital plane has to be "edge on" to the observer. If an observer was looking at the star from above or below, he would not detect any planets.

That means you only have a very narrow range of planetary orbital planes that allow detection; since we've discovered thousands of new worlds - that means there's a *lot* of planets out there.

By definition transits can only occur when the observer is on the orbital plane. From any other vantage point the transit isn't seen and so couldn't be recorded by the instruments used to measure the luminosity of the star, and so there wouldn't be any transit evidence of the exoplanet. They still might be detected spectroscopically (red/blue spectral shift) or visually by measuring the wobble.

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Exoplanets search methods took care of them all.