On the other hand: mặt khác, một mặt … mặt khác

Mặt khác means "the other side", and it opens a sentence that looks at the matter from another side: Mặt khác, chi phí đầu tư ban đầu còn cao. On the other hand, the initial investment is still high.

Unlike English "on the other hand", it doesn't have to contrast. Very often it simply adds a second point or reason, closer to "besides" or "moreover": Chính sách này giúp giảm ùn tắc. Mặt khác, nó còn góp phần giảm ô nhiễm. This policy helps ease congestion. Besides, it also helps cut pollution. The words around it tell you which: còn or cũng signals an extra point, while nhưng or lại signals a contrast.

The paired frame một mặt …, mặt khác … (on the one hand …, on the other …) sets two sides next to each other in one sentence. They may pull against each other, or both may be things that need doing: Một mặt phải bảo đảm tăng trưởng, mặt khác phải kiểm soát lạm phát. Growth must be ensured, and at the same time inflation kept in check.

You'll meet it mostly in university papers, essays and opinion pieces, and much less in ordinary news reports. For a clear contrast, news prefers tuy nhiên (however); for a plain extra point, bên cạnh đó (besides). In conversation, people say với lại (and anyway) to add a reason, or nhưng mà for a contrast.