The difference is that the ball bearing is rolling on a circular track instead of sliding. When analyzing the motion we must take into account the moment of inertia of the ball bearing.
In a simple pendulum the bob rotates about the pivot point. This is equivalent to sliding (without friction) on the circular track. But the ball-bearing pendulum is rotating about its own centre as it also rotates about the imaginary pivot point at the centre of the circular track.
For a certain amplitude of swing, there is a fixed amount of energy. At the lowest point the kinetic energy of the ball bearing is divided between linear motion of the CM and rotation about the CM, whereas for the simple pendulum bob it all goes into linear motion of the CM. So the linear speed of the CM of the ball bearing is slower than that of the simple pendulum bob, resulting in a longer period for the ball bearing. When we come to measure the period, it is only the back-and-forth motion of the CM which we measure; we ignore the rotation of the ball bearing.
According to Oscillation of a rolling sphere in a bowl, the period of small oscillations is
$$T=2\pi \sqrt{\frac{7R}{5g}}=1.1832T_0$$
where $T_0$ is the period of a simple pendulum of the same length $R$. In the lecture $T_0=1.85s$ so we should expect $T=2.19s$. We can only assume the remaining difference with the measured value of $2.27s$ is due to other errors - eg the measurement of $R$.
Accuracy can mean different things. While the question asks about the statistical accuracy, what immediately comes when talking about the Newton's laws is that they are non-relativistic, i.e., they are valid up to small corrections of order $v/c$.
Physics laws are based on empirical observations, the symmetries of the universe, and approximations appropriate for a given situation.
Symmetries
For example, we have reasons to think that conservation of momentum or energy are exact laws, since they follow from the symmetry of space in respect to translations in space and time (Noether's theorem). Testing these laws in practice will necessarily result in statistical errors, but improving the precision of measurement is unlikely to uncover any discrepancies.
Approximations
Newton's laws are valid only in non-relativistic limit. Thus, they will hold only up to small corrections of order $v/c$ where $v$ is the speed of the object and $c$ is the speed of light. If our relative statistical precision (in measuring the force, acceleration, etc.) is of order $v/c$, we will observe deviations.
Empirical observations
Laws of thermodynamics are a good example of the laws that were deduced phenomenologycally, as a result of many observations. Yet, statistical physics shows that they hold up to very high precision ($\sim 1/N\sqrt{N_A}$, where $N_A$ is the Avodagro constant). If the precision could be so high or when dealing with systems where the number of particles is not small, we will observe deviations from these laws.
Remark
I recommend the answer by @AdamLatosiĊski, which is technically probably more correct than mine. What I tried to explain in my answer is how the laws of physics are different from, e.g., the biological laws (since the subject was recently debated on this site) - the latter are generalizations of many statistical observations, but not grounded in reasoning about fundamental properties of the universe. They are therefore statistical laws, which are bound to be non-exact. Indeed, even the so-called Central dogma of molecular biology ($DNA\rightarrow RNA \rightarrow Protein$) is broken by some viruses, performing reverse transcription ($RNA\rightarrow DNA$.)
Best Answer
This quite special top is called a rattleback, or celt. See Wikipedia : http://en.wikipedia.org/wiki/Rattleback
I quote : "The spin-reversal motion follows from the growth of instabilities on the other rotation axes, that are rolling (on the main axis) and pitching (on the crosswise axis). (...) The amplified mode will differ depending on the spin direction, which explains the rattleback's asymmetrical behavior. Depending on whether it is rather a pitching or rolling instability that dominates, the growth rate will be very high or quite low."
You can find some for sale or even build your own : http://www.iop.org/EJ/abstract/0143-0807/11/1/112