Is the information in the warnings true?

The answer in a nutshell: no.

Do the "Blue Star" tattoos exist?
No. LSD is not packaged in the form of lick-and-stick tattoos, and I have seen no evidence of LSD having ever been found in this form. The rumors are the result of confusion: LSD is commonly packaged as small squares of blotter-paper that have been soaked in a solution containing LSD. These blotter-paper squares are sometimes marked with an identifying trademark (e.g. blue unicorns, Bart Simpson) printed on the blotter-paper. In 1980, a police report of a bust by the Narcotics Bureau of the New Jersey State Police referred to this marking of blotter acid as "stamps" and noted that "children may be susceptible to this type of cartoon stamp believing it a tattoo transfer."
(Examples of blotter acid)
Can LSD be absorbed through the skin?
Yes, but in the circumstances described in the warning flyers -- casual handling of blotter acid, or "tattoos" -- this is extremely unlikely.
What about the stamps, the "micro dot," or the "window pain?"
LSD, as well as being packaged as blotter-paper, is also sold in a liquid solution, in a gelatin medium (known as "windowpane") and as pills or capsules (known as "microdot"). Some flyers insist that there are "stamps" or "tattoos" with pictures of multi-colored "micro dots" or "window panes" on them. Just confusion.
And the red cardboard box wrapped in foil?
These were details included in the police report from 1980 mentioned above. They have been commonly included in the flyers ever since, but just happen to be where one unlucky set of LSD users hid their stash. Heat and light degrade LSD, so some users use foil to wrap their blotter acid as protection from the elements.
Are the cartoon characters used to lure kids into the drug scene?
Cartoon characters are sometimes used as the trademarks printed on blotter acid, but I doubt this is like "Joe Camel" being used to target a younger audience, although the motivations of those who pick the trademarks aren't public knowledge. I have seen pictures of blotter acid marked with Bart Simpson (from the cartoon "The Simpsons") and Mickey Mouse (in his role as the sorcerer's apprentice from the movie "Fantasia"), but note that these characters are popular with both adults and children. There is little to be gained for a drug dealer or manufacturer from getting a child to inadvertantly try LSD. The child isn't likely to want to repeat what will probably be a frightening and baffling experience, he or she doesn't have as much cash to pay for drugs as do adults, and a frying child will certainly catch the eyes of the authorities.
But if they try it once, they might get hooked, right?
LSD is not an addictive drug. In fact, there is a temporary tolerance built up to the effects of LSD (meaning that subsequent doses, if taken within a few days, will have a substantially blunted effect) which makes it, if anything, anti-addictive.
Doesn't LSD react quickly?
Depends on what you mean by quickly. Blotter acid usually starts showing effects between 45 and 90 minutes after the dose is taken.
And is it laced with strychnine?
Blotter acid is not laced with strychnine. This is another urban legend, taken as gospel truth even by many LSD users. This deserves its own FAQ, but until then, check out the explanation at the Lycaeum (but see also this analysis from alt.folklore.urban).
Might the accidental ingestion of LSD be fatal?
The fatal dose of LSD is fairly enormous compared to the active dose. The drug is active in the hundreds of micrograms range (a dose that conveniently fits on a small piece of blotter paper). The only fatalities or near-fatalities from LSD overdose that I know about happened when a quantity of purified LSD in crystal form was mistaken for another drug (cocaine or speed, probably) and was snorted, probably giving the unfortunate user hundreds of doses. (see: this page for details). In the circumstances described in the warning flyers, an overdose would be extremely unlikely, if not impossible.

However, even a small dose, given to an unprepared or unwilling subject, could cause enough disorientation to make it dangeous for the subject in situations where hand-eye coordination or attention are necessary for survival (driving a bicycle in traffic, for instance). The emotional upheaval occasionally caused by "bad trips" can possibly lead to suicide, and this risk is heightened if the user doesn't know what to expect, isn't accompanied by people who have had experience with psychedelics, or has been dosed without knowing about it.

What are the symptoms associated with LSD use?
Too complex a question to answer here, try searching around the web for the many sites devoted to this question. A good start is the Lycaeum's LSD page which has the text of LSD discoverer Albert Hofmann's book on the subject, and many other FAQs and links.
Have any children died from these tattoos?
No. Haven't you been paying attention? The tattoos don't exist.
What about the authorities who issued the warning?
A lot of them prove hard to track down. Mr. Guy Chaillé and J. O'Donnel, for instance, don't exist, or at least they can't be found at the institutions they allegedly sent the warnings from. Beth Israel Medical Center, Danbury Hospital, and other sources deny having issued the warnings. This isn't to say that all of these authorities are just fabricated. Police departments and hospitals get fooled by this legend just like the rest of us. And some of the people who deny having had anything to do with it may just be trying not to look foolish.
Should I contact the police if I see these tattoos?
No. You should contact me! I want to hear about it! For that matter, I'd appreciate it if you'd let me know if you see a warning flyer. And if you could pick one up and mail it to me, that'd be an extra thrill for me. I love this stuff!
Should I spread the warning far and wide?
Please do!