Of course, the first reason that age limits are put on toys is for safety. That is always one concern. You will always want to make sure that your child can't choke on small pieces on the toy.
A second reason to pay attention to the age appropriate labels is for developmental reasons. Kids should be able to be allowed to explore their toys on their own from time to time. You should always supervise, but you may not be right there to activate the toys or help the child in whatever way necessary. When kids (especially 1-2 year olds) are on their own, they will abandon a toy if it gets too difficult. Therefore, having toys that are above their developmental level is of no use because he/she will walk away from it before "learning" anything through exploration. A child who is placed with toys at his/her developmental level, however, will play with the toys for an extended period of time and learn through discovery.
Older children, when faced with a toy that is above his/her developmental level, can simply become frustrated. My little cousin was trying to play with a remote control truck, but it was really too hard for him when he was 3. He became frustrated and threw the truck. So instead of leaving the truck for another toy, his mother had to diffuse the situation that had resulted in anger and frustration.
Now, notice that I have said "developmental" level and not age level. You must know your child and know what developmental level he/she is at when choosing toys. If your child is behind motorically, then you may want a simpler toy that requires gross motor skills rather than fine motor skills. If your child excels in this area, then you can probably give him/her more advanced toys. The same goes for language development. The toys that are too easy for your child may still be enjoyable, but your child will not be challenged or will not learn anything new from it. You have to make the call as to when it is time to put the toy away - either to hold onto it for the next child or give it away. If you are not sure what level your child is at, then simply place toys in his/her play area and watch. You will be able to see what your child is interested in (my son loves books, blocks, puzzles, and cars) and what toys are appropriate for him/her to play with on his own.
Don't get rid of the toys that are too hard. One thing you can do is put them away for later. You could also put them in a spot out of sight for your child and take them out when you have time to help your child with them. This will give your child a "new experience" and you will be helping to teach your child the skill that he/she is lacking to operate the toy on his/her own.
Another thought is that battery operated toys typically need an adult's help to operate. Try to find non-battery operated toys for when your child is playing on his/her own.