Can I break my lease if the dates on it are incorrect?

A typographical error on a contract, including a lease, does not provide grounds to declare it void; as long as there is evidence of, for example, the term the contract or lease should have covered, courts will treat the error as what it is--a typo or clerical mistake.

However, you may have grounds to get out of the lease if (1) there are security concerns traceable to landlord's activities, which landlord is not addressing (e.g.  not securing common areas properly); or (2) landlord is otherwise denying you the "quiet enjoyment" or use of your property, or otherwise him/herself violating key lease terms. However, security concerns that "just" go to a bad neighborhood will not get you out of the lease, if the landlord is being reasonable in what he/she is doing in terms of security.