I have written potential revisions in italics.

I think it is really important to remember and learn from the past. 

First of all, the error of the past is the wisdom and success of the future. 

Errors we make in the past give us the wisdom we need to succeed in the future.

We all make mistakes; learning from* the past can help us to find out the reasons behind them and avoid making the same mistakes in the future. 

* I wouldn't say that learning from the past is what helps us discover the reason behind our mistakes, but rather examining or reflecting upon helps us discover the reason behind our mistakes. It is after examining or reflecting upon the past that we actually learn from it.

We all make mistakes. Reflecting on the past can help us discover the cause of our mistakes so that we can avoid making the same errors in the future.

(A semicolon is also okay in this situation.)

As a result, we are more likely to achieve our goal**. 

It is not enough to simply go through a lot of difficult experiences. In order to make progress, we must carefully examine these experiences and think about how we can apply what we learned to help us reach our goals.

** Most people have more than one goal in life.

Second, studying the past enables us to build upon our* predecessors’ achievements. There is no need to repeat basic research*** or to reinvent the wheel. 

*** You could be a little more specific here. I can't really imagine what "basic research" is . . .

* The word "predecessor" is usually used with a possessive pronoun. I'm not sure why this is, but I think it's because it's related to the word "precede," which is (what I would describe as, anyway) comparative. 

X preceded Y <=> X is Y's predecessor

Some alternatives to "our predecessors' achievements" would be:

[our] former achievements

[our] past achievements

[our] previous achievements

I put "our" in brackets because you can include it or leave it out. 

Instead, we should learn from the accomplishments made in the past and then improve upon them.

We should instead spend our time learning from their successes as well as their failures and try to improve upon the product laid before us.