What are some examples of how Lennie is a hard worker but also a dangerous man?

Lennie is most definitely a hard worker.  This is the key to his survival, and George knows that if Lennie is given a chance to show his willingness to work, his disabilities might be overlooked.  In their first meeting with the boss the conversation reflects this attitude:

The boss pointed a playful finger at Lennie. "He ain't much of a talker, is he?"

"No, he ain't, but he's sure a hell of a good worker....

Lennie is most definitely a hard worker.  This is the key to his survival, and George knows that if Lennie is given a chance to show his willingness to work, his disabilities might be overlooked.  In their first meeting with the boss the conversation reflects this attitude:

The boss pointed a playful finger at Lennie. "He ain't much of a talker, is he?"

"No, he ain't, but he's sure a hell of a good worker. Strong as a bull."

Lennie smiled to himself. "Strong as a bull," he repeated.

After his first day in the fields, Slim comments on Lennie's desire to please with his hard work:

“Say, you sure was right about him. Maybe he ain’t bright, but I never seen such a worker. He damn near killed his partner buckin’ barley. There ain’t nobody can keep up with him. God awmighty, I never seen such a strong guy.” 

But as both these quotes demonstrate, Lennie's work ethic is always tied to his almost supernatural strength.  While he has a pure and gentle heart, his strength causes him to do unintentional harm on several occasions, beginning with the mice he likes to carry in his pocket:

"They was so little," he said apologetically. "I’d pet ‘em, and pretty soon they bit my fingers and I pinched their heads a little and then they was dead—because they was so little."

This event is mirrored later in the book after Lennie is given a puppy:

"He was so little," said Lennie. "I was jus playin’ with him… an’ he made like he’s gonna bite me… an’ I made like I was gonna smack him … an’… an’ I done it. An’ then he was dead."

His accidental violence is, unfortunately, not limited to animals.  When Curley takes his frustration out on Lennie after being embarrassed by the other men in the bunkhouse, Lennie responds:

Curley’s fist was swinging when Lennie reached for it. The next minute Curley was flopping like a fish on a line, and his closed fist was lost in Lennie’s big hand. 

Lennie's ultimate act of violence, though--the one that led to his inevitable death--is against Curley's wife:

And she continued to struggle, and her eyes were wild with terror. He shook her then, and he was angry with her. “Don’t you go yellin’,” he said, and he shook her; and her body flopped like a fish. And then she was still, for Lennie had broken her neck.

While Lennie is incredibly strong and is able to channel that strength into his work on the fields, he can not contain it when in stressful situations.  His mental incapacities will not allow him the ability to see past his present circumstances to understand the consequences of his actions.