请找出下面的短文中的语法错误，并改正它们。

The weather was nice, it was warm and sunny out. Timothy went on a walk with his dog, they played some fetch and enjoyed the fresh air. After a while, Timothy's dog became very tired, so him and his dog went back home. Them spent the rest of the day resting.
原文中有多处语法错误：

1. 句子 "so him and his dog went back home" 应为 "so he and his dog went back home" 。这是由于 "so" 是连接词，连接的是后面的句子，所以要用主格形式的 "he"。
2. 句子 "Them spent the rest of the day resting" 应为 "They spent the rest of the day resting"，因为"they" 是主语，而不是"them"。

改正后的文本为：

The weather was nice. It was warm and sunny out. Timothy went on a walk with his dog. They played some fetch and enjoyed the fresh air. After a while, Timothy's dog became very tired, so he and his dog went back home. They spent the rest of the day resting.