Here are a few of the common problems woodwind doublers have with the clarinet:
Flabby/saggy/tubby/airy tone and flat pitch. This is a dead giveaway for a self-“taught” clarinet doubler. The clarinet’s voicing is quite high, higher than any of the other woodwinds, and beginning clarinetists sometimes struggle for years to make that proper voicing a consistent habit. Once it settles in, pitch problems mostly evaporate, tone becomes clear and ringing, and notes respond beautifully and easily in every register. If you’re thinking about buying a shorter barrel because your “clarinet” is so flat all the time, don’t. Work on your voicing instead. Voicing is the #1 crucial technique for successful clarinet doubling, and will solve most of your problems.
It may also be worth checking your mouthpiece angle—it should be quite steep compared to saxophone or double reed instruments. Keep your head up straight and eyes forward, and aim in the ballpark of keeping the clarinet around 30° from vertical. You can also use the paper trick to make sure you’re taking in the right amount of mouthpiece.
Reeds can be a contributing factor, too. Often (but not always) saxophonists lean toward a slightly more open mouthpiece and softer reed, while clarinetists lean toward a little more closed mouthpiece and stiffer reed. The strength you prefer on a typical saxophone mouthpiece may not be right strength for a typical clarinet mouthpiece.
Constricted tone. Bafflingly, there’s a common pedagogical idea that clarinetists should tighten their embouchures to fix various problems. This is nonsense. Keep your jaw open to make space for the reed to vibrate, and let your lips (not your jaw/teeth) close around the mouthpiece, not tight but just airtight. Notes will respond more readily, with a fuller, prettier tone, and you can throw away the tape or paper or dental appliance you have been using to cushion your lower lip from your teeth.
Squeaks. 95% of the time this is an issue of fingers failing to properly cover toneholes. (And 95% of the time, struggling clarinet doublers blame it on something having vaguely to do with embouchure, reeds, or the clarinet somehow just being a squeaky instrument.) Use the large, fleshy pads of your fingers (not the tippy-tips) to cover the holes. Sometimes a quick check in the mirror can reveal that your fingers aren’t where you think they are.
Fingering awkwardness. The clarinet’s fingering system and unique overtone series provide tremendous advantages: an expansive range, clean and precise technique, and lots of useful alternate fingerings. (It’s superior to the saxophone’s “easier” system with awkward palm keys and relatively few alternates. Fight me.)
But if you’re coming from another instrument, you might find the 12th between the lower and clarion registers confounding. That’s because you’re still thinking about the fingerings. Practice your scales, arpeggios, and études until your fingers move on autopilot, like they already do on your primary instrument. It can be done.
The clarinet’s dreaded “break” as a technique concern is mostly a myth. Keep your support, voicing, and embouchure well-formed and stable, and just move your fingers. Your left index finger should rock or tilt between its tonehole and the A key, not hop (losing contact with the instrument) or slide (dragging along the key). Work toward a tiny, efficient, relaxed movement.
The clarinet’s clever system of redundant pinky keys enables lightning-fast technique in virtually any key, but it takes real effort to learn to use them well. Remember that for those pinky-finger notes there aren’t really “standard” vs. “alternate” fingerings—you need to know them all well enough to use interchangeably. And if you have beginner habits like using both pinkies for third-line B, you will need to learn to use a single pinky in many cases for the most efficient and flexible approach.
Ledger line catastrophes. Because of the clarinet’s broad tessitura, clarinetists have to be fluent in ledger lines above the staff (maybe more than you’re used to if you’re an oboist) and below the staff (more than you’re used to on any treble-clef woodwind). Hit the Baermann or Kroepsh books for thorough workouts spanning the clarinet’s range.
Remember the best money you can spend on your clarinet playing isn’t another mouthpiece or barrel or book—it’s some lessons with an excellent teacher. Learn the instrument on its own terms, and, whatever you do, try not to sound like a doubler.
I find the right pinky B/E is impossible for me to finger and use effectively. Luckily I have a left E-flat/A-flat key which helps.