Always evaluate your work before handing it in. Ways of doing this include:
Play both parts together on a piano, while listening to the harmonic intervals (if something sounds "wrong," it often is);
Play and sing each line by itself to judge its melodic character (does it seem aimless? Is there a goal? Is there a single high-note?).
When playing/singing the individual lines, do so relatively quickly; it gives you a better feel for the overall contour.
Write each harmonic interval between voices in this and remaining species .
This may seem pedantic, but it makes you more aware of any harmonic interval problems your counterpoint may have; being aware of these problems provides the opportunity to fix them.
Examples of 'harmonic interval problems' include:
Dissonances (none allowed, and don't forget that a perfect 4th is a dissonance);
Not mixing up perfect and imperfect intervals enough;
Overuse of one particular interval (like 5 or more 3rds in a row, for example);
Three or more perfect intervals in a row;
Parallel, hidden, or consecutive 5ths or 8ves; or
Unisons somewhere other than the first or last notes.
Avoid exceeding a tenth between parts, because one goal is to keep the voices relatively close together.
Jeppesen says: “Only for the sake of a beautiful voice leading should the interval of the tenth be exceeded.” (p.112).
A voice can repeat a note once per exercise in first species, but both voices should not repeat notes at the same time. Similarly, if one voice skips an octave, the other voice should not simultaneously repeat a note (or skip an octave).
Occasional voice-crossing is characteristic of the style. However, if both voices skip simulataneously to the previoius notes in the other voice (i.e., if one voice jumps from E down to middle C while the other
jumps from middle C up to E; see example below), the listener hears a repetition of a harmonic interval, which is similar to both voices repeating notes simultaneously, and thus should be avoided:
sounds like:
If there is no voice-crossing (e.g., if the first interval is a tenth and the second interval a sixth, or vice-versa), it is not an issue:
The two voices should be essentially distinct from one another. It is not uncommon to have both voices move in parallel motion for two or three (Schubert's text allows four) notes, especially approaching the cadence, but the general goal is to create two melodic lines that are distinct in shape.
Contrary motion is not always possible or even desirable, but aim to have it occur at least 50% of the time.
The preferred cadence (by far) is the Clausula Vera ("true," or "authentic" cadence),
where the final is approached by step from above and below in the two voices. The second choice is to cadence on the fifth in the upper voice
(the lower voice always cadences on the final), but this occurs much less often than the clausula vera.
Also, the melodic fragment “so-ti-do” is to be avoided at cadences due to its association with tonal music.
Review cadential approaches to the final if in doubt.
Unisons may occur only on the first or last notes of an exercise in first species.
Review the difference between direct (AKA "hidden") fifths and octaves (D5, D8), and consecutive 5ths and 8ves (C5, C8; AKA "5ths or 8ves by contrary motion").
Neither is permissible:
Aim to have a melodic span of about an octave in the part you write, but bear in mind that it may not always be feasible in first species if the given cantus firmus is relatively short
(8 - 10 notes), as in the Jeppesen text. You should still aim to create a relatively wide melodic span, however. A span of a P4th, for example, is still unacceptable.
sounds like: 
