Q:

How to select recent errors that were raised in an SQL-Server database?

is there a way to do something like:
select top 100 * from sys.recent_raised_errors order by date
My scenario was that I had an application that executed a stored procedure in the database, and after installing a new trigger on a table,  that procedure had an error raised inside of it, that caused the app to crash. It was obvious to me that the app is crashing due to a DB issue, but I had to debug the app or read its logs to find out what went wrong in the stored procedure.

A:

try to do below step:
In Object Explorer, connect to an instance of the SQL Server and then expand that instance.
Find and expand the Management section 
Right-click on SQL Server Logs, select View, and choose View SQL Server Log. 

Or you can start profile to tracking the exception
I just did a testing with SQL Profiler

Create a tiger that will get a exception.
CREATE TRIGGER trig_test
    ON  dbo.T
    AFTER INSERT,DELETE,UPDATE
AS 
BEGIN
    SET NOCOUNT ON;
    SELECT 1/0
END
GO
INSERT INTO dbo.T( remark )VALUES  ( '')

The following is the message that got from Profiler.

