Step 1: Release the handbrakes
... if a bit slow
SELECT to_char(MIN(ts)::timestamptz, 'YYYY-MM-DD HH24:MI:SS TZ') AS min_time
      ,SUM(CASE WHEN sensor_id = 572 THEN value ELSE 0.0 END) AS nickname1
      ,SUM(CASE WHEN sensor_id = 542 THEN value ELSE 0.0 END) AS nickname2
      ,SUM(CASE WHEN sensor_id = 571 THEN value ELSE 0.0 END) AS nickname3
FROM   sensor_values
-- LEFT JOIN sensor_values_cleaned s2 USING (sensor_id, ts)
WHERE  ts >= '2013-10-14T00:00:00+00:00'::timestamptz::timestamp
AND    ts <  '2013-10-18T00:00:00+00:00'::timestamptz::timestamp
AND    sensor_id IN (572, 542, 571, 540, 541, 573)
GROUP  BY ts::date AS day
ORDER  BY 1;
Major points
- Replace reserved words (in standard SQL) in your identifiers.
 - timestamp->- ts
 - time->- min_time
 
- Since the join is on identical column names you can use the simpler - USINGclause in the join condition:- USING (sensor_id, ts)
 However, since the second table- sensor_values_cleanedis 100% irrelevant to this query, I removed it entirely.
 
- As @joop already advised, switch - min()and- to_char()in your first out put column. This way, Postgres can determine the minimum from the original column value, which is generally faster and may be able to utilize an index. In this specific case, ordering by- dateis also cheaper than ordering by a- text, which would also have to consider collation rules.
 
- A similar consideration applies to your - WHEREcondition:
 - WHERE  ts::timestamptz >= '2013-10-14T00:00:00+00:00'::timestamptz
 - WHERE  ts >= '2013-10-14T00:00:00+00:00'::timestamptz::timestamp
 - The second one is sargable and can utilize a plain index on - ts- to great effect on performance in big tables!
 
- Using - ts::dateinstead of- date_trunc('day', ts). Simpler, faster, same result.
 
- Most probably your second WHERE condition is slightly incorrect. Generally, you would exclude the upper border:
 - AND    ts <=  '2013-10-18T00:00:00+00:00' ...
 
 - AND    ts <   '2013-10-18T00:00:00+00:00' ...
 
- When mixing - timestampand- timestamptzone needs to be aware of the effects. For instance, your- WHEREcondition doesn't cut at 00:00 local time (except if local time coincides with UTC). Details here:
 Ignoring timezones altogether in Rails and PostgreSQL
 
Step 2: Your request
...the difference between the latest and earliest timestamps in each grouping
And by that I suppose you mean:
...the difference between the value of  the latest and earliest timestamps ...
Otherwise it would be much simpler.
Use window functions for that, in particular first_value() and last_value(). Careful with the combination, you want a non-standard window frame for last_value() in this case. Compare:
PostgreSQL aggregate or window function to return just the last value
I combine this with DISTINCT ON, which is more convenient in this case than GROUP BY (which would need another subquery level):
SELECT DISTINCT ON (ts::date, sensor_id)
       ts::date AS day
      ,to_char((min(ts)  OVER (PARTITION BY ts::date))::timestamptz
              ,'YYYY-MM-DD HH24:MI:SS TZ') AS min_time
      ,sensor_id
      ,last_value(value)    OVER (PARTITION BY ts::date, sensor_id ORDER BY ts
                     RANGE BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)
       - first_value(value) OVER (PARTITION BY ts::date, sensor_id ORDER BY ts)
                                                                   AS val_range
FROM   sensor_values
WHERE  ts >= '2013-10-14T00:00:00+0'::timestamptz::timestamp
AND    ts <  '2013-10-18T00:00:00+0'::timestamptz::timestamp
AND    sensor_id IN (540, 541, 542, 571, 572, 573)
ORDER  BY ts::date, sensor_id;
-> SQLfiddle demo.
Step 3: Pivot table
Building on the query above I use crosstab() from the additional module tablefunc:
SELECT * FROM crosstab(
   $$SELECT DISTINCT ON (1,3)
            ts::date AS day
           ,to_char((min(ts) OVER (PARTITION BY ts::date))::timestamptz,'YYYY-MM-DD HH24:MI:SS TZ') AS min_time
           ,sensor_id
           ,last_value(value)    OVER (PARTITION BY ts::date, sensor_id ORDER BY ts RANGE BETWEEN UNBOUNDED PRECEDING AND UNBOUNDED FOLLOWING)
            - first_value(value) OVER (PARTITION BY ts::date, sensor_id ORDER BY ts) AS val_range
     FROM   sensor_values
     WHERE  ts >= '2013-10-14T00:00:00+0'::timestamptz::timestamp
     AND    ts <  '2013-10-18T00:00:00+0'::timestamptz::timestamp
     AND    sensor_id IN (540, 541, 542, 571, 572, 573)
     ORDER  BY 1, 3$$
   ,$$VALUES (540), (541), (542), (571), (572), (573)$$
   )
AS ct (day date, min_time text, s540 numeric, s541 numeric, s542 numeric, s571 numeric, s572 numeric, s573 numeric);
Returns (and much faster than before):
    day     |         min_time         | s540  | s541  | s542  | s571  | s572  | s573
------------+--------------------------+-------+-------+-------+-------+-------+-------
 2013-10-14 | 2013-10-14 03:00:00 CEST | 18.82 | 18.98 | 19.97 | 19.47 | 17.56 | 21.27
 2013-10-15 | 2013-10-15 00:15:00 CEST | 22.59 | 24.20 | 22.90 | 21.27 | 22.75 | 22.23
 2013-10-16 | 2013-10-16 00:16:00 CEST | 23.74 | 22.52 | 22.23 | 23.22 | 23.03 | 22.98
 2013-10-17 | 2013-10-17 00:17:00 CEST | 21.68 | 24.54 | 21.15 | 23.58 | 23.04 | 21.94