Vermithrax]Even if you're innocent, any statements made to police can be used against you along with "mistaken or unreliable evidence" to get a conviction against you.
I had a case the other day where two witnesses swore they saw my client at a particular time and place. They got on the stand and said they were 100% positive. A police officer got on the stand and swore that he saw my client.
Evidence later comes out that all three were 100% dead wrong. Luckiest part for my client is that he would have lost at trial -- no questions asked.