If "validation failure" means that there is some client error in the request, then use HTTP 400 (Bad Request). For instance if the URI is supposed to have an ISO-8601 date and you find that it's in the wrong format or refers to February 31st, then you would return an HTTP 400. Ditto if you expect well-formed XML in an entity body and it fails to parse.

(1/2016): Over the last five years WebDAV's more specific HTTP 422 (Unprocessable Entity) has become a very reasonable alternative to HTTP 400. See for instance its use in JSON API. But do note that HTTP 422 has not made it into HTTP 1.1, RFC-7231.

Richardson and Ruby's RESTful Web Services contains a very helpful appendix on when to use the various HTTP response codes. They say:

400 (“Bad Request”)
Importance: High.
This is the generic client-side error status, used when no other 4xx error code is appropriate. It’s commonly used when the client submits a representation along with a PUT or POST request, and the representation is in the right format, but it doesn’t make any sense. (p. 381)

and:

401 (“Unauthorized”)
Importance: High.
The client tried to operate on a protected resource without providing the proper authentication credentials. It may have provided the wrong credentials, or none at all. The credentials may be a username and password, an API key, or an authentication token—whatever the service in question is expecting. It’s common for a client to make a request for a URI and accept a 401 just so it knows what kind of credentials to send and in what format. [...]

I noticed this question a couple of days late, but I feel that I can add some insight. I hope this can be helpful towards your RESTful venture.

Point 1: Am I understanding it right?

You understood right. That is a correct representation of a RESTful architecture. You may find the following matrix from Wikipedia very helpful in defining your nouns and verbs:

When dealing with a Collection URI like: http://example.com/resources/

• GET: List the members of the collection, complete with their member URIs for further navigation. For example, list all the cars for sale.

• PUT: Meaning defined as "replace the entire collection with another collection".

• POST: Create a new entry in the collection where the ID is assigned automatically by the collection. The ID created is usually included as part of the data returned by this operation.

• DELETE: Meaning defined as "delete the entire collection".

When dealing with a Member URI like: http://example.com/resources/7HOU57Y

• GET: Retrieve a representation of the addressed member of the collection expressed in an appropriate MIME type.

• PUT: Update the addressed member of the collection or create it with the specified ID.

• POST: Treats the addressed member as a collection in its own right and creates a new subordinate of it.

• DELETE: Delete the addressed member of the collection.

Point 2: I need more verbs

In general, when you think you need more verbs, it may actually mean that your resources need to be re-identified. Remember that in REST you are always acting on a resource, or on a collection of resources. What you choose as the resource is quite important for your API definition.

Activate/Deactivate Login: If you are creating a new session, then you may want to consider "the session" as the resource. To create a new session, use POST to http://example.com/sessions/ with the credentials in the body. To expire it use PUT or a DELETE (maybe depending on whether you intend to keep a session history) to http://example.com/sessions/SESSION_ID.

Change Password: This time the resource is "the user". You would need a PUT to http://example.com/users/USER_ID with the old and new passwords in the body. You are acting on "the user" resource, and a change password is simply an update request. It's quite similar to the UPDATE statement in a relational database.

My instinct would be to do a GET call to a URL like /api/users/1/activate_login

This goes against a very core REST principle: The correct usage of HTTP verbs. Any GET request should never leave any side effect.

For example, a GET request should never create a session on the database, return a cookie with a new Session ID, or leave any residue on the server. The GET verb is like the SELECT statement in a database engine. Remember that the response to any request with the GET verb should be cache-able when requested with the same parameters, just like when you request a static web page.

Point 3: How to return error messages and codes

Consider the 4xx or 5xx HTTP status codes as error categories. You can elaborate the error in the body.

Failed to Connect to Database: / Incorrect Database Login: In general you should use a 500 error for these types of errors. This is a server-side error. The client did nothing wrong. 500 errors are normally considered "retryable". i.e. the client can retry the same exact request, and expect it to succeed once the server's troubles are resolved. Specify the details in the body, so that the client will be able to provide some context to us humans.

The other category of errors would be the 4xx family, which in general indicate that the client did something wrong. In particular, this category of errors normally indicate to the client that there is no need to retry the request as it is, because it will continue to fail permanently. i.e. the client needs to change something before retrying this request. For example, "Resource not found" (HTTP 404) or "Malformed Request" (HTTP 400) errors would fall in this category.

Point 4: How to do authentication

As pointed out in point 1, instead of authenticating a user, you may want to think about creating a session. You will be returned a new "Session ID", along with the appropriate HTTP status code (200: Access Granted or 403: Access Denied).

You will then be asking your RESTful server: "Can you GET me the resource for this Session ID?".

There is no authenticated mode - REST is stateless: You create a session, you ask the server to give you resources using this Session ID as a parameter, and on logout you drop or expire the session.