I think it will only have a negative effect if there is no adult supervision involved. Children will explore everything in their environment and test how people respond to their behavior. So if no one will guide them, they wouldn't know which of the things that they are exploring are good and bad for them.
Agree with Sam --- one of the ways they explore something is by tasting it! So if there isn't an adult around, your toddler could accidentally eat dirty or even dangerous things. Parents have to be careful too -- toddlers are surprisingly fast and trip way too easily when they want to go exploring.
I do agree on what's said above. If I were you, I'd be feeling lucky that my kid loves to feed his curiosity. I've read that this is one sign of multiple intelligence. I think for as long as you are always there to guide, I think there shouldn't be something to worry about.
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