Suzuki Roshi used the word "should" a lot, maybe more than he should have. Sometimes I felt like what he was saying would have been expressed better with could or would or will. Often it was clearly what he meant as in the following lecture when, for some reason, tea was served:

When you drink tea, you should not listen to a lecture. I'm sorry, but it is true. When you listen to a lecture, you should listen, just listen to the lecture. That is our way. When we talk, we should not take tea like this. We cannot do two things at one time, because each activity includes everything. When you take tea it includes all of your activity and covers all of your activity. This our practice. - 66-01-21-BN - This quote also reinforces this point on DC on SR.

and the following makes sense with should as do all his uses of it, but this could be would or will

If we are alert enough, wise enough, we should take care of ourselves with alertness, not fall into the pitfall of human nature. We have many dangers in our life, and sometime we know it and sometimes we do not know it. So it is necessary for us to have some rules to protect ourselves. - 66-01-21-A

and this:

Dogen Zenji said, “Think unthinkable.” We think, but the direction of our thinking is opposite. Instead of trying to attain something, we try to forget. Instead of keep thinking, we try to stop thinking. What you will acquire through this practice will be tremendous, and every activity should be based on this kind of readiness of your mind. So all the practice, Rinzai or Soto, or five or seven schools of Zen, and many other practices should be based on this power. - 67-12-05-A

and did he really mean "should" in the following and not "will."

Especially when you do something good, you know-- supposed to be good, you suffer more [laughs]. When you do something by mistake, you don't suffer. “This is by mistake, so I will not  make the same mistake again.” That's all. But if you try to do something good, or you did something which is supposed to be good, because you did something with some idea of good and bad, you suffer more. Especially by the idea of good, you suffer more [laughs] -- you should suffer more [laughs]. That is good experience. Okay? - 69-09-00-B

It seemed he liked the word, but also, in foreign languages we easily get into what are called fossilized habits. In the current transcript collection of Shunryu Suzuki lectures on shunryusuzuki.com, there are 480 instances of the word would, 771 of could, and 5312 of should. He did get questions about his use of this word. Some people fretted terribly over the nuance of a usage - none more than "should." Some seemed to feel it was language suited more to a wrathful god or demanding outside power. "There are no shoulds," was a popular saying back then. Sometimes after such a question he'd back off it a little but he'd be just as likely to insist that that's what he meant or to come back later with more shoulds stressed forcefully, seeming a bit pissed off at the resistance, at us not getting the heart of what he was saying and instead complaining about a detail of his delivery that didn't suit us. They sure don't have a tradition of questioning teachers that way in Japan. No need to worry about it though. We may make of it what we prefer or just read or listen on and let big mind sort it out. - dc

These excerpts edited by DC and posted 12-18-14