To determine the correct observation depths for using a current meter to measure flow velocity in a stream with a depth of 1 m, we need to understand the standard practice for such measurements. In fluid mechanics and water resources engineering, measuring the velocity of the flow at specific depths allows for an accurate determination of the average velocity.

1. Standard Depths for Measurement: For streams and rivers, the standard practice is to measure flow velocities at particular depths to accurately calculate the mean velocity. Commonly, measurements are taken at two different points, which are often chosen to be \(0.2D\) and \(0.8D\) of the total depth \(D\).
2. Justification for Choosing 0.2D and 0.8D: In hydrology, it is empirically established that measuring at 20% (0.2) and 80% (0.8) of the depth provides a reliable estimation of the average velocity across the section. This method accounts for the velocity distribution, which typically decreases towards the bed and the surface.
3. Calculation for Depths in this Question: Given the total depth \(D = 1 \text{ m}\), the measurement should be taken at \(0.2 \times 1 = 0.2 \text{ m}\) and at \(0.8 \times 1 = 0.8 \text{ m}\).
4. Ruling Out Incorrect Options: The options provided that suggest measurements at \(0 \text{ depth}\) or at \(0.2 \text{ and } 0.6 \text{ depth}\) do not align with the empirical practices for accurate flow measurement using current meters, which are based on the velocity profile of flowing water.

Conclusion: Therefore, the best practice for this scenario, given the stream depth of 1 m, is to measure the flow velocity at 0.2 m and 0.8 m. Thus, the correct answer is at 0.2 and 0.8 depth of flow.