Getting wrong values for other columns when I select MAX(updated_date)

You either need a GROUP BY clause or a more complex query.

SELECT field1, MAX(updated_date)  FROM mytable GROUP BY field1

For the sample data, this will return 3 rows.

More likely, you want:

SELECT t1.field1, t3.max_date  FROM mytable AS t1  JOIN (SELECT MAX(t2.updated_date) AS max_date          FROM mytable AS t2       ) AS t3    ON t1.updated_date = t3.max_date;

For the sample data, this will return 1 row:

ta3   2012-03-11 11:05:56

Of the major DBMS, only MySQL allows you to omit the GROUP BY clause when you have a mixture of aggregates and non-aggregate columns in the select-list. The SQL standard requires the GROUP BY clause and you must list all non-aggregate columns in it. Sometimes, in MySQL, omitting the GROUP BY clause produces the answer you want; as often as not, though, it manages to give an unexpected answer.

Use ORDER BY and LIMIT.
Then it's as simple as:

  SELECT field1, updated_date     FROM mytableORDER BY updated_date DESC    LIMIT 1;

If the query is needed a lot you can try this alternative:

  SELECT t1.field1, t1.updated_date     FROM mytable t1         LEFT JOIN mytable t2      AND t2.updated_date > t1.updated_date   WHERE t2.field1 IS NULL;

Short explanation:
For each row, give me any rows with a more-recent updated_date.
But (WHERE clause) take only the row with no more-recent updated_date.
The technique is sometimes called a self-exclusion join.
This is the intermediate result (without WHERE clause, and adding t2.* to SELECT list):

ta1    2012-03-11 11:05:15    ta2     2012-03-11 11:05:32ta1    2012-03-11 11:05:15    ta3     2012-03-11 11:05:56ta2    2012-03-11 11:05:32    ta3     2012-03-11 11:05:56ta3    2012-03-11 11:05:56    null    null