Vue.js API integration errors can be caused by various factors such as incorrect API endpoint URL, authentication issues, network errors, or server-side errors. Here are some common issues and solutions:

1. Incorrect API Endpoint URL: Make sure you're using the correct URL for your API. Typos and misspellings in the URL can cause issues. Also, ensure that the URL is correctly formatted and includes the necessary parameters if required by the API.

2. Authentication Issues: If your API requires authentication, make sure you have the correct credentials and follow the API documentation to authenticate your requests. For example, you may need to include an Authorization header with a valid token in your request.

3. Network Errors: Ensure that you have an active internet connection and that your API server is running properly. Also, check if there are any network-level issues such as firewalls or proxies blocking the connection to your API server.

4. Server-side Errors: If you're receiving a server error message, it can be helpful to check the server logs for more details on what might be causing the error. Some common server errors include 404 (Not Found) and 500 (Internal Server Error).

5. Cross-Origin Resource Sharing (CORS): If your API is located on a different domain than your Vue.js application, you may need to configure CORS settings on your server to allow cross-origin requests from your Vue.js app.

6. Using Axios for HTTP Requests: Axios is a popular library used in Vue.js for making HTTP requests. Make sure that you're using the correct syntax and options when making API calls with Axios. For example, you can set headers or query parameters using the Axios headers and params properties.

7. Using Fetch API: The fetch API is another popular method for making HTTP requests in Vue.js. Make sure that you're handling promises correctly and using the correct syntax when making API calls with fetch.

8. Caching Issues: If your API returns cached data, it can cause issues in your Vue.js app. Consider clearing cache or adding headers to your API request to prevent caching.

If you continue to have difficulty fixing API integration errors, it may be helpful to consult with a web developer or the API documentation for further assistance.