Outputting Errors to User

I currently am making a small application where a user will enter their ID which needs to be in a certain format. When entered in the wrong format, different output errors are produced.

I currently output errors like this:

public void errorLogger(string error)
        {
            errors += error + Environment.NewLine + "";
        }

I have read that using += is not a great operator to use. Alternatively I have thought this may be better:

public void errorLogger(string key, string err)
        {
            if(!String.IsNullOrEmpty(err))
            output.Add(key, err);
        }

but then I basically do the same thing later:

string keys = "";
    foreach (KeyValuePair entry in core.errorLogger())
    {
        keys += entry.Key + ":       " + entry.Value + "";
    }

Is there a cleaner way to output errors? The output is injected under the submit button into:

errorSpan.InnerHtml = (keys);

This is what I ended up using going off of Charles' response to AWinkle

public void logError(string err, string desc)
                {
                    if(!String.IsNullOrEmpty(desc))
                        errors.AppendFormat("{0,10}: {1}", err, desc);
                }
public string getErrors()
            {
                return errors.ToString();
            }

Then :

errorspan.InnerHtml = (core.getErrors());

Using the StringBuilder class will typically be better for looped string building.

string keys = "";
foreach (KeyValuePair entry in core.errorLogger())
{
    keys += entry.Key + ":       " + entry.Value + "";
}

turns into

StringBuilder keys = new StringBuilder();
foreach (KeyValuePair entry in core.errorLogger())
{
    keys.AppendFormat("{0}: {1}", entry.Key, entry.Value);
}

Then you take errorSpan.InnerHtml = (keys); and change it to errorSpan.InnerHtml = (keys.ToString());

Alternatively, you could use this to replace the dictionary as CharlesNRice suggests.

StringBuilder keys = new StringBuilder();

 public void errorLogger(string key, string err)
    {
        if(!String.IsNullOrEmpty(err))
        keys.AppendFormat("{0}: {1}", key,err);
    }

StackExchange Code Review Q#69194, answer score: 4