Select ALL fields that contains only UPPERCASE letters

You may want to use a case sensitive collation. I believe the default is case insensitive. Example:

CREATE TABLE my_table (
   id int,
   name varchar(50)
) CHARACTER SET latin1 COLLATE latin1_general_cs;

INSERT INTO my_table VALUES (1, 'SomeThing');
INSERT INTO my_table VALUES (2, 'something');
INSERT INTO my_table VALUES (3, 'SOMETHING');
INSERT INTO my_table VALUES (4, 'SOME4THING');

Then:

SELECT * FROM my_table WHERE name REGEXP '^[A-Z]+$';
+------+-----------+
| id   | name      |
+------+-----------+
|    3 | SOMETHING |
+------+-----------+
1 row in set (0.00 sec)

If you don't want to use a case sensitive collation for the whole table, you can also use the COLLATE clause as @kchau suggested in the other answer.

Let's try with a table using a case insensitive collation:

CREATE TABLE my_table (
   id int,
   name varchar(50)
) CHARACTER SET latin1 COLLATE latin1_general_ci;

INSERT INTO my_table VALUES (1, 'SomeThing');
INSERT INTO my_table VALUES (2, 'something');
INSERT INTO my_table VALUES (3, 'SOMETHING');
INSERT INTO my_table VALUES (4, 'SOME4THING');

This won't work very well:

SELECT * FROM my_table WHERE name REGEXP '^[A-Z]+$';
+------+-----------+
| id   | name      |
+------+-----------+
|    1 | SomeThing |
|    2 | something |
|    3 | SOMETHING |
+------+-----------+
3 rows in set (0.00 sec)

But we can use the COLLATE clause to collate the name field to a case sensitive collation:

SELECT * FROM my_table WHERE (name COLLATE latin1_general_cs) REGEXP '^[A-Z]+$';
+------+-----------+
| id   | name      |
+------+-----------+
|    3 | SOMETHING |
+------+-----------+
1 row in set (0.00 sec)

This worked for me. It found all user emails with uppercase character:

SELECT * FROM users WHERE mail REGEXP BINARY '[A-Z]';

SELECT * FROM table1 WHERE (columnname COLLATE latin1_bin )=UPPER(depart);