有点儿 / 一点儿【yǒudiǎnr / yìdiǎnr】

Both mean "a bit". What separates them is where they sit and what they imply.

有点儿 goes before the adjective and says the speaker is not happy about it.

一点儿 goes after the adjective and asks for an adjustment, or states a small difference.

Swapping them gives zhè ge这个cài菜yī diǎn r5一点儿Xián咸 and qǐng请yǒu diǎn r5有点儿màn shuō慢说, both wrong.

有点儿 is for things you'd rather were otherwise

贵, 累, 难, 咸, 远 – these take 有点儿 easily. A good thing normally does not: yǒu diǎn r5有点儿piào liang漂亮 sounds odd, because there is nothing to complain about.

一点儿 after an adjective is a comparison

慢一点儿 is slower than the current speed, 便宜一点儿 is cheaper than the price just quoted. That is why it works as a polite request.

有一点儿 is the full form

有点儿 is the contraction of 有一点儿, and both are correct.

The 儿 is optional

有点 and 一点 are the same words without the northern ending.