In general a clean and strong recording is best. You want the signal (bird song) to stand out above any noise, and also to be isolated from other bird sounds or other noises.
That said, modern smart phones/tablets and Song Sleuth together do a good job of picking out faint sounds, and the app is capable of identifying moderately distant sounds. Overlapping bird sounds in a chorus are definitely a challenge (but for some species that are often found in noisy flocks, e.g. Canada Goose, Common Grackle, etc, the app has been trained to recognize the flock chorus). In all cases using the Isolate Song interface to draw a tight box around the song of interest will help to isolate one sound and allow the app to work better.