为什么了。
Tom does speak Chinese well, but his reading and writing skills leave much to be improved.
这句话中实际上是两句独立的话，用 but 做转折连接了。你可以把第二部分做独立的句子来理解。
his reading and writing skills 是主语
leaves 做谓语
leaves much to be improved 说的是：他的阅读和写作技能还有很多需要提高的空间
该理解为：被提高
他的阅读和写作技能需要被提高。
With a lot of difficult problems to settle, the manager felt worried all the time.
这句话是一句话，不是两句话，这句话的主语是 the manager
With a lot of difficult problems to settle 做状语使用，表述一个原因 = Because the manager needed to settle a lot of difficult problems, the manager felt worried all the time.
cheers
