zero is not needed, one or two HW errors a minute is fine, but I found the L3+ is more sensitive to HW errors, as your average hashrate will lower once you get too many.
It's a bit different on the D3, as it the D3 can still run fine when having upto 10 HW errors a minute or so.
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So I tried keeping it to a couple errors a minute, but I endedup with asic errors, after I reset the boards everything went back to normal, whew. It's strange cause my D3 runs fine wother 550 mhz each board with no errors and one of the boards is as 16V and it's running at 74C, I guess I got the winter to thank for that. But yeah I'm trying to run a maximum overclock, but this L3 is being a pain so far.

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The L3 is great for running at a lower voltage at a nice overclock, but it doesn't overclock as good as the D3 does. 640 - 700 MH/s is really the limit from what I've seen so far.
ASIC errors just indicate you clocked it too high (for the voltage set). Don;t worry, it won't kill your ASIC's permanently.