The LD50 is around 60mg/mL. That means around half of a mL of 100mg/mL can kill you! I'm talking about horrible nicotine overdose, then heart palpitations, then death. This is the concentration that can kill you, let alone enough to make you sick.
If you have ever seen a 1mL syringe then you know- its not that much.
I just feel a need to point out that, while the warning here is good, it's probably just a bit exaggerated. The LD50 for nicotine is around .5 to 1.0 mg/kg for adults, meaning that 50% of people weighing 150 pounds, for example, would die from ingesting 32 to 64mg of nicotine. So, yes, it's highly toxic, but two factors work in the favor of your typical DIYer:
First, there's the ingestion part. It'd be difficult to accidentally ingest that much nicotine. While nicotine does transfer relatively easily through skin, in a spill the amount of nicotine which would be absorbed into the skin would obviously be quite a bit less than the amount spilled.
The second factor in our favor is that, as vapers and ex-smokers, we have a higher tolerance for nicotine than most people. The LD50 is an average for all people, with or without resistance, which means that an LD50 amount of nicotine is not likely to kill people like us who come into contact with nicotine every day.
That said, people have died from skin contact with nicotine. It's rare, but it happens. What's much more likely is a really bad headache, possibly some vomiting, and you'll
really wish you'd been more careful once you're functional again. But a half ml of 100mg/ml juice is highly unlikely to kill any of us, unless we're drinking it.
But yes, I totally agree it's something to be very careful with.