Code review: a buggy bounded buffer

A teammate wrote this buffer for EdgeCampus frames. It "works in testing" but occasionally loses frames, occasionally hangs, and once threw an exception.

class FrameBuffer {
    private final Frame[] buf = new Frame[64];
    private int in = 0, out = 0, count = 0;

    public void put(Frame f) throws InterruptedException {
        synchronized (this) {
            if (count == buf.length) wait();
        }
        buf[in] = f;
        in = (in + 1) % buf.length;
        count++;
        synchronized (this) { notify(); }
    }

    public synchronized Frame take() throws InterruptedException {
        if (count == 0) wait();
        Frame f = buf[out];
        out = (out + 1) % buf.length;
        count--;
        notify();
        return f;
    }
}

1. Find at least four concurrency bugs; for each, give a concrete interleaving or scenario that causes a visible failure (lost frame, hang, exception, wrong frame).
2. Rewrite the class correctly using a monitor (synchronized, wait, notifyAll).
3. Rewrite it in one line using a class from java.util.concurrent, and explain when you would still prefer your own implementation.