Whether it's safe to spray neem is an important question to ask. There are several issues here...
Not all insects are bad. Does neem spray make a difference between bad and good bugs?
And what about spraying neem in the vegetable garden? How long do you have to wait until you can eat your tomatoes?
Please only use neem spray in the very early morning or late afternoon, or you may hurt beneficial insects. Neem oil is not toxic to them but it can suffocate them if you spray them directly and the soap can hurt them too.
You should only spray neem at times when insects are not active. Once the spray has dried it is not harmful to good insects any more, only to sucking and chewing bugs.
As long as you use a home made spray with pure neem oil (product link) it is totally safe. (If using a premade commercial spray, read the label carefully. Some products contain the usual insecticides and only have some neem added on top of that.)
There is no need for protective clothing or anything like that when using home made sprays. You can even use neem oil spray on yourself! People use the more concentrated mixtures as a safe and natural insect repellent. It's much better for you than the harmful DEET.
Not only that, it is actually good for your skin. Really.
Neem spray can be used on your fruits and vegetables. You can spray vegetables and fruit trees with home made neem spray right up until the day of harvest. Also, there are no herbs, vegetables or fruit trees that are sensitive to oil sprays.
Soil drenches are designed to get the plant to absorb the neem oil through the roots. There are some vegetables, like oinons, cabbages, and tomoatoes, that apparently do not like soil drenches with raw neem oil. Spraying, however, is fine.
Neem is generally safe for all plants, both edible and ornamental. However, all oils can do injury to sensitive plants. 0.5% is a low enough concentration to avoid that, but be careful if plants are drought stressed, when the humidity is high, or during periods of extreme heat or cold.
Do a test application before you use neem oil spray on plants that are known to be sensitive to oils: impatiens, fuchsias, hibiscus and some roses, trees like maples, hickories or black walnut.
If used correctly, during the early morning or late afternoon, and not during humid weather or on drought stressed plants, you should be fine. But don't take my word for it. Always test your mix before you spray neem on new plants!
Learn more about making, using and buying neem insect spray.