If you're willing to take your astronaut's helmet off for a minute, below is a lightweight logger I've written for Silverlight, for client-side logging (for use mainly with WCF operations but could be for any errors).
It was originally used in Monotouch for iPhone apps, and has been adapted for IsolateStorage. You can use the Read method to display in a textbox if needed. Tested in SL4.
/// <summary>
/// A lightweight logging class for Silverlight.
/// </summary>
public class Log
{
    /// <summary>
    /// The log file to write to. Defaults to "dd-mm-yyyy.log" e.g. "13-01-2010.log"
    /// </summary>
    public static string LogFilename { get; set; }
    /// <summary>
    /// Whether to appendthe calling method to the start of the log line.
    /// </summary>
    public static bool UseStackFrame { get; set; }
    static Log()
    {
        LogFilename = string.Format("{0}.log", DateTime.Today.ToString("dd-MM-yyyy"));
        UseStackFrame = false;
    }
    /// <summary>
    /// Reads the entire log file, or returns an empty string if it doesn't exist yet.
    /// </summary>
    /// <returns></returns>
    public static string ReadLog()
    {
        string result = "";
        IsolatedStorageFile storage = IsolatedStorageFile.GetUserStoreForSite();
        if (storage.FileExists(LogFilename))
        {
            try
            {
                using (IsolatedStorageFileStream stream = new IsolatedStorageFileStream(LogFilename,FileMode.OpenOrCreate,storage))
                {
                    using (StreamReader reader = new StreamReader(stream))
                    {
                        result = reader.ReadToEnd();
                    }
                }
            }
            catch (IOException)
            {
                // Ignore
            }
        }
        return result;
    }
    /// <summary>
    /// Writes information (not errors) to the log file.
    /// </summary>
    /// <param name="format">A format string</param>
    /// <param name="args">Any arguments for the format string.</param>
    public static void Info(string format, params object[] args)
    {
        WriteLine(LoggingLevel.Info, format, args);
    }
    /// <summary>
    /// Writes a warning (non critical error) to the log file
    /// </summary>
    /// <param name="format">A format string</param>
    /// <param name="args">Any arguments for the format string.</param>
    public static void Warn(string format, params object[] args)
    {
        WriteLine(LoggingLevel.Warn, format, args);
    }
    /// <summary>
    /// Writes a critical or fatal error to the log file.
    /// </summary>
    /// <param name="format">A format string</param>
    /// <param name="args">Any arguments for the format string.</param>
    public static void Fatal(string format, params object[] args)
    {
        WriteLine(LoggingLevel.Fatal, format, args);
    }
    /// <summary>
    /// Writes the args to the default logging output using the format provided.
    /// </summary>
    public static void WriteLine(LoggingLevel level, string format, params object[] args)
    {
        string message = string.Format(format, args);
        // Optionally show the calling method
        if (UseStackFrame)
        {
            var name = new StackFrame(2, false).GetMethod().Name;
            string prefix = string.Format("[{0} - {1}] ", level, name);
            message = string.Format(prefix + format, args);
        }
        Debug.WriteLine(message);
        WriteToFile(message);
    }
    /// <summary>
    /// Writes a line to the current log file.
    /// </summary>
    /// <param name="message"></param>
    private static void WriteToFile(string message)
    {
        try
        {
            IsolatedStorageFile storage = IsolatedStorageFile.GetUserStoreForSite();
            bool b = storage.FileExists(LogFilename);
            using (IsolatedStorageFileStream stream = new IsolatedStorageFileStream(LogFilename,FileMode.Append,storage))
            {
                using (StreamWriter writer = new StreamWriter(stream))
                {
                    writer.WriteLine("[{0}] {1}", DateTime.UtcNow.ToString(), message);
                }
            }
        }
        catch (IOException)
        {
            // throw new Catch22Exception();
        }
    }
}
/// <summary>
/// The type of error to log.
/// </summary>
public enum LoggingLevel
{
    /// <summary>
    /// A message containing information only.
    /// </summary>
    Info,
    /// <summary>
    /// A non-critical warning error message.
    /// </summary>
    Warn,
    /// <summary>
    /// A fatal error message.
    /// </summary>
    Fatal
}