The Washington Redskins gave an exhibition worthy of the preseason tonight. They stumbled through a mistake-ridden performance against the Miami Dolphins that should make Coach Joe Gibbs' next squad cuts that much easier.

"We were our own worst enemy," said Gibbs. "There probably will be some people who played well, but we had a lot of breakdowns in some crucial areas. If you turn the ball over like that, you aren't going to beat anybody."

About the only thing the Redskins didn't botch was a midfield pregame handshake with the Dolphins that was supposed to show union solidarity. But any solidarity the Redskins had with each other during the game was hard to detect as Miami pulled away to a 24-7 victory.

Many in the crowd at the Orange Bowl booed the handshakes but cheered lustily in the second half, when the Dolphins broke a 7-7 tie with the help of some particularly crucial Washington errors.

The Redskins weren't completely inept. For the first 15 minutes, with quarterback Joe Theismann looking sharp, they were the superior team. But once Gibbs began substituting, the advantage swung to Miami.

Gibbs will have to look no further than the statistics sheet to find the reasons for this defeat. He'll find these negative numbers: three fumbles lost, two interceptions, seven sacks, 92 yards in penalties, all climaxed by Dolphin defensive end Ed Weaver's 28-yard touchdown run in the last two minutes after recovering Tom Flick's fumble.

Poor Flick. He was victimized by a porous offensive line and rarely had much time to pass. In one series, he and backup center Ron Saul, moving over from guard, even had problems getting the snap timed correctly.

"It was very discouraging for us to play like that," Gibbs said. "We had worked hard in camp, but it showed we have a long way to go . . . The only good thing about it was it didn't count."

Gibbs didn't go all out to win. But after what he considered a good week of practice at the team's Carlisle, Pa., training camp, he was optimistic the Redskins wouldn't embarrass themselves against the Dolphins, who have a history of using mostly first-stringers in preseason games.

But Gibbs was wrong. Especially in the second half, the Redskins looked pathetic. They threatened to score only once after intermission, but mistakes quickly eliminated that opportunity.

The Dolphins shook off a slow start to play better and better as the game pro-gressed, even when third-string quarterback Jim Jensen was directing the offense.

While the Dolphins were getting untracked, the Redskins played sharply. They took the lead, 7-0, a two-yard run by John Riggins with 5:36 left in the first quarter. The touchdown was set up by a roughing the kicker penalty on Miami's Paul Lankford, who knocked over Mark Moseley after the latter had missed a 53-yard field goal attempt.

Theismann jumped on that mistake. On first down, he passed 26 yards to receiver Art Monk, who had run a fine curl-in pattern in front of Lankford. Earlier in the drive, Riggins (13 yards) and Joe Washington (11 yards) had been able to get outside Miami's defense.

After the touchdown, Redskins heroes were harder to find. Theismann's 12-yard swing pass to Clarence Harmon helped set up a 48-yard field goal try by rookie Dan Miller, but the kick appeared to be blocked and fell short of the goal posts.

Miami first scored after two pass interference calls against strong safety Mike Nelms in the last three minutes of the first half.

Nelms also was victimized by the key play in the drive, Jensen's 35-yard pass to tight end Joe Rose, who pulled in the ball after it bounced off his chest, rolled down his arm and almost fell off his fingers. His catch gave the Dolphins a first down at the Washington 14.

Then Jensen passed to receiver Elmer Bradley at the nine. Bradley shook off a tackle by rookie cornerback Vernon Dean, Washington's No. 2 draft choice, and ran into the end zone with 17 seconds left in the second period.

The Dolphins didn't have to wait long the next half to go ahead for good. Linebacker Larry Gordon intercepted Flick on the first series, returning the ball to his 44, where veteran quarterback Don Strock began a touchdown march with a 20-yard pass over the middle to a wide-open Duriel Harris.

Three plays later, Rose outleaped free safety Mark Murphy for a 19-yard reception at the two. Fullback Andra Franklin then powered over for the touchdown.

Murphy, however, made Washington's best defensive play of the game. In the first half, he picked off a long pass and returned it 15 yards.

A fumble by Harmon that was protested vigorously by Gibbs gave the Dolphins the ball again at midfield, but free agent kicker Jorge Portela failed on a 43-yard field goal attempt.

Gibbs tried to help out Flick by even calling a flea-flicker, but a third-down sack resulted in another Redskin punt. The Dolphins then moved 74 yards on 12 plays, mostly behind the running of impressive rookie Larry Cowan, to set up a 24-yard field goal by another rookie free agent, Rex Robinson, for a 17-7 lead.

Miami completed the runaway on Weaver's fun run. Flick was back trying to pass when Weaver, a rookie from Georgia who was one of eight Dolphins not to participate in the midfield handshake, knocked the ball out of the quarterback's hands and ran with it.

Gibbs and his staff didn't gain much from having the kickers compete. Mike Connell and Jeff Hayes both had two punts, none distinguished. Both kicked off into the end zone. Miller and Moseley failed on their field goal tries, although Miller made his conversion kick.

The Redskins' performance undoubtedly would have been better had Gibbs not substituted as liberally in the second half. Although he had said he would go longer than last year with his veterans, he appeared to pull them just as quickly as in 1981. Miami's drive for the second-half field goal came against a unit that included third-string cornerbacks.

"We wanted to play people for purposes of evaluation," Gibbs said. "We had to look at a lot of people at a lot of positions."

The Redskins had three players hurt during the game. Receiver Cris Crissey broke his jaw, which will require surgery. Tight end Clint Didier bruised a thigh and cornerback LeCharls McDaniel got a concussion.