Right... back to the topic at hand...
Remember foremost that it's a Valse (Waltz). Which means the downbeat is everything. The other two beats are frosting for the next downbeat. So make your shifts and string crossings butter smooth and let the stuff after each downbeat kind of roll into the next one. This can be difficult, especially in places like measures 9 and 10 (the first four measures are rests, remember) where there's a climactic note way off beat. Without a pulse and dead-on intonation, those measures sound like noodling and it's very frustrating when you're trying to make it flow. A good way to emphasize the downbeats besides dynamics is to make the initial vibrato very wide right on the beat, and then immediately relax it. Especially on the half and dotted half notes.
Also, try this in practice, but not in performance: overplay it. Meaning, *really* emphasize the beats, do crazy thick vibrato, slide on up to the high notes like those in measures 7, 15 and 16, put a giant fermata on that high quarter note in measure 28 (or even the other lead-in notes, like measure 32), like you have all the time in the world - play it like a drunk Italian tenor would sing it (but in tune). Playing along those lines was actually performance practice in Koussevitsky's day, and you can see how this piece lends itself to that kind of schmaltz. Modern performance finds such playing sloppy (which it is), so don't learn it that way, but giving it a whirl at tempo could inform your performance and help it sing.
Speaking of tempo, never play it any faster than you can play it smoothly. It's easier to get it smooth at, say, quarter note=92 and increase the speed from there rather than learn how hit all the notes at tempo and try to smooth them out afterwards. This is true for all music, but especially for a piece like this whose entire charm is its ability to flow like melted butter. Good luck.
