The sound, rhythm, and intonation are crucial to the correct performance of Tannhäuser. The two main sections, rehearsal letters "A" and "M," are quite similar, but their differences should to be observed very carefully. One would be wise to learn both passages thoroughly for an audition.
At letter "A", which is in 3/4, a steady tempo is very important in order to keep the excerpt moving. The triplets need to be kept strictly in tempo; they often drag and therefore create a delay in the rythmical line. The dotted-eighth, sixteenth rhythms on the third beats need to be precisely subdivided so that they are executed correctly. A full tone is required in this section. One has to work up the stamina to play this with a consistent tone quality and without note or rhythm errors. Too often, these little details are overlooked, and this can make the difference between success and failure in both auditions and performance.
At letter "M," because the note values of the theme are augmented, it is important to focus on breathing in order to keep the phrase as full as possible. There should not be a dimuendo on each note, rather, play through them. Keep in mind the direction and goal of the phrase. The triplets should be as even as possible and should not drag. Some attention should be given to the last few bars of the piece, as it could be asked on an audition for the sake of endurance. In order to keep a warm and big sound, this excerpt shouldn't be played excessively loud, even though it is marked ff. The effect of the ff should be divided among the members of the low brass section. There are a lot of other interesting things going on in the orcherstra, they should be able to be heard in addition to the brass.
I suggest practicing this excerpt as one would play an etude from the Joannes Rochut Melodious Etudes. This means in a singing style, very legato and at a lesser dynamic level to make sure that the tune becomes very natural for the trombonist. Such practice will enable the player to perform the excerpt over and over again without completely ruining his or her embouchure. While playing this excerpt in the orchestra, one has to concentrate on a whole different set of problems, especially with the intonation, as everybody is playing very loud and not always in their most comfortable register. Good luck!