I think you need to add...
AND outside.asset_tag=inside.asset_tag
...to the criteria in your ON list.
Also a RIGHT OUTER JOIN is not needed. An INNER JOIN will give the same results (and may be more efficicient), since there will be cannot be be combinations of asset_tag and last_read_date in the subquery that do not exist in mp_vehicle_asset_profile.
Even then, the query may return more than one row per asset tag if there are "ties" -- that is, multiple rows with the same last_read_date. In contrast, @Lamak's analytic-based answer will arbitrarily pick exactly one row this situation.
Your comment suggests that you want to break ties by picking the row with highest mtr_reading for the last_read_date.
You could modify @Lamak's analyic-based answer to do this by changing the ORDER BY in the OVER clause to:
ORDER BY last_read_date DESC, mtr_reading DESC
If there are still ties (that is, multiple rows with the same asset_tag, last_read_date, and mtr_reading), the query will again abritrarily pick exactly one row.
You could modify my aggregate-based answer to break ties using highest mtr_reading as follows:
SELECT
outside.asset_tag,
outside.description,
outside.asset_type,
outside.asset_group,
outside.status_code,
outside.license_no,
outside.rentable_yn,
outside.manufacture_code,
outside.model,
outside.manufacture_vin,
outside.vehicle_yr,
outside.meter_id,
outside.mtr_uom,
outside.mtr_reading,
outside.last_read_date
FROM
mp_vehicle_asset_profile outside
INNER JOIN
(
SELECT
asset_tag,
MAX(last_read_date) AS last_read_date,
MAX(mtr_reading) KEEP (DENSE_RANK FIRST ORDER BY last_read_date DESC) AS mtr_reading
FROM
mp_vehicle_asset_profile
GROUP BY
asset_tag
) inside
ON
outside.asset_tag = inside.asset_tag
AND
outside.last_read_date = inside.last_read_date
AND
outside.mtr_reading = inside.mtr_reading
If there are still ties (that is, multiple rows with the same asset_tag, last_read_date, and mtr_reading), the query may again return more than one row.
One other way that the analytic- and aggregate-based answers differ is in their treatment of nulls. If any of asset_tag, last_read_date, or mtr_reading are null, the analytic-based answer will return related rows, but the aggregate-based one will not (because the equality conditions in the join do not evaluate to TRUE when a null is involved.