《牛津英语用法指南》第三版第570节指出：

在 suggest 后面的 that 从句中，如果建议某人该做某事，各种动词形式都可以用。 

a 可以用普通的现在时和过去时。

Her uncle suggests that she gets a job in a bank. 她叔叔建议她在银行里找份工作。

He suggested that she got a job in a bank.他曾建议她在银行里找份工作。

b 常用 should +不带 to 的动词不定式。

He suggests that she should get a job in a bank.他建议她在银行里找份工作。

He suggested that she should get a job in a bank.他曾建议她在银行里找份工作。

c 也可以用虚拟语气（参见567），特别是在美国英语中。

He suggests that she get a job in a bank.他建议她在银行里找份工作。

He suggested that she get a job in a bank.他曾建议她在银行里找份工作。

在直接的建议（ I suggest ...）中，一般不用 should 。I suggest (that) you get ... 我建议你找 ......（不能说：I suggest that you should get ...）”

suggest表示“建议”时，它后面的宾语从句应该要用虚拟语气吧！也就是用 should+动词原形。我有时也看到没有用虚拟语气而用了陈述语气，这算是错吗？

回答如下：

(1)suggest 提议;建议 用虚拟语气

主语(A)+suggest that 主语(B)+(should) do sth

I suggest that you (should )ask him some specific questions about his past.

我建议你问他一些有关他的过去的具体问题。

He suggested that we should come another day.   
他建议我们改天来。

She suggested that Brooks might go to Chicago and try to find a job there.  
她建议布鲁克斯到芝加哥去,设法在那里找个工作。

Facer suggests that we walk home.   
费塞建议我们步行回家。

I suggest that we leave early for the airport.   
我提议早点去机场。

They suggested we should visit a class right away.   
他们建议我们马上去听课。

I suggest you investigate the case again.   
我建议你们再调查一次。

The doctor suggested he go for a holiday.   
医生建议他去度假休息一阵子。

I suggest he adapt himself to his new conditions.   
我建议他使自己适应新的环境。

The letter suggested that a new clinic be built.   
那封信建议新建一座诊所。

(2)suggest暗示，表明，用陈述语气

主语(A)+suggest that 主语(B)+do sth

Earlier reports suggested that a meeting would take place on Sunday..

早先的报道暗示周日可能会召开会议。

Her expression suggested that she was angry.   
她的表情说明她生气了。

The mistakes in your exercise books suggest that you have not paid enough attention to grammar.   
你练习本上的错误说明你对语法注意不够。

Its institutional tone suggested that it was written in the foreign office.   
它的官方口吻说明它是在外交部写的。

Tiny rippling whirlpools on the water's surface suggest that the ponds are full of fish.   
水面的小漩涡说明池塘里尽是鱼。