There's no particular performance issue (beyond the cost of loading a class via the classloader - negligible)
The above does create an anonymous class and as such it contains an implicit this
reference to the surrounding instance. That can cause some confusion for serialisation frameworks. e.g. you serialise the anonymous class you've created, and you suddenly find you're also trying to serialise the containing instance.
I would highlight that anonymous classes can be used a lot under the covers in different frameworks and indeed languages (Scala - I'm looking at you). I've never heard anyone suggest that Scala has issues with performance due to classloading. Initial startup may be fractionally slower, but bear in mind JVM startup, JIT warmup, any network access etc.
You might argue that your application footprint is bigger, due to more classes. I suspect (again) the effect is negligible (unless you construct a whole application out of anonymous classes!)